Chapter 17: worked solutions and marking guide
35 review answers and 35 exam answers
Chapter review solutions
A 10 cm by 8 cm by 14 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 4 cm by 2 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 3 cm, 5 cm and 5 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(3+5+5)=52 cm.
A 12 cm by 8 cm by 7 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 3 cm by 4 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 6 cm, 6 cm and 8 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(6+6+8)=80 cm.
A 13 cm by 6 cm by 15 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Draw one connected, foldable six-face net of a 6 cm by 5 cm by 2 cm cuboid. Label each face with its dimensions.
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
A cuboid has side lengths 6 cm, 7 cm and 8 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(6+7+8)=84 cm.
A 5 cm by 16 cm by 4 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Draw one connected, foldable six-face net of a 5 cm by 3 cm by 2 cm cuboid. Label each face with its dimensions.
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
A cuboid has side lengths 4 cm, 3 cm and 6 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(4+3+6)=52 cm.
A 12 cm by 3 cm by 10 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 3 cm by 5 cm by 4 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 3 cm, 4 cm and 8 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(3+4+8)=60 cm.
A 4 cm by 3 cm by 15 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 4 cm by 3 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 5 cm, 7 cm and 8 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(5+7+8)=80 cm.
A 15 cm by 11 cm by 5 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 4 cm by 5 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 5 cm, 8 cm and 4 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(5+8+4)=68 cm.
A 4 cm by 17 cm by 9 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 5 cm by 2 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 5 cm, 5 cm and 5 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(5+5+5)=60 cm.
A 10 cm by 3 cm by 21 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Draw one connected, foldable six-face net of a 4 cm by 3 cm by 6 cm cuboid. Label each face with its dimensions.
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
A cuboid has side lengths 3 cm, 5 cm and 7 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(3+5+7)=60 cm.
A 14 cm by 9 cm by 17 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 3 cm by 4 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid has side lengths 2 cm, 8 cm and 7 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(2+8+7)=68 cm.
A 3 cm by 16 cm by 17 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
A cuboid measures 2 cm by 6 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A 9 cm by 16 cm by 16 cm cuboid has how many faces, edges, and vertices? Explain or sketch the mathematical relationship.
Count six rectangular faces, twelve meeting segments and eight corner points. State which quantities or geometric properties justify the method.
A learner draws six correct rectangles for a 4×6×3 cuboid but leaves them as six unconnected pieces. Is that a complete net? Explain.
Matching face sizes are necessary but not sufficient: a net is a connected planar arrangement that folds into the cuboid.
A cuboid has side lengths 5 cm, 7 cm and 4 cm. Find the combined length of all twelve edges. Explain or sketch the mathematical relationship.
There are four of each dimension. Total = 4×(5+7+4)=64 cm. State which quantities or geometric properties justify the method.
Practice examination solutions
A 11 cm by 7 cm by 4 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 2 cm, 7 cm and 7 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(2+7+7)=64 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 5 cm by 11 cm by 18 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 4 cm by 2 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 3 cm by 2 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 4 cm, 8 cm and 9 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(4+8+9)=84 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A cuboid has side lengths 2 cm, 5 cm and 7 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(2+5+7)=56 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A cuboid measures 4 cm by 5 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 2 cm, 3 cm and 8 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(2+3+8)=52 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 14 cm by 9 cm by 16 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 4 cm by 5 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 4 cm, 3 cm and 5 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(4+3+5)=48 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A cuboid measures 4 cm by 3 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 2 cm, 3 cm and 5 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(2+3+5)=40 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A cuboid measures 4 cm by 6 cm by 5 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A 2 cm by 4 cm by 18 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 3 cm, 4 cm and 4 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(3+4+4)=44 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A cuboid has side lengths 6 cm, 8 cm and 8 cm. Find the combined length of all twelve edges. Explain or sketch the mathematical relationship.
There are four of each dimension. Total = 4×(6+8+8)=88 cm. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A 10 cm by 14 cm by 7 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 6 cm by 2 cm by 4 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 4 cm, 8 cm and 6 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(4+8+6)=72 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 5 cm by 12 cm by 16 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A 5 cm by 3 cm by 14 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A 7 cm by 9 cm by 16 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 2 cm by 4 cm by 5 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 5 cm by 6 cm by 4 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid measures 5 cm by 4 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A 5 cm by 3 cm by 9 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Draw one connected, foldable six-face net of a 6 cm by 5 cm by 4 cm cuboid. Label each face with its dimensions.
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Does a 15-cm long rectangular box have 8 or 12 vertices? Explain.
A vertex is a corner; there are four corners on each of two opposite rectangular ends.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A 6 cm by 17 cm by 13 cm cuboid has how many faces, edges, and vertices? Explain or sketch the mathematical relationship.
Count six rectangular faces, twelve meeting segments and eight corner points. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A 10 cm by 17 cm by 14 cm cuboid has how many faces, edges, and vertices?
Count six rectangular faces, twelve meeting segments and eight corner points.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A cuboid has side lengths 7 cm, 5 cm and 6 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(7+5+6)=72 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Does a 7-cm long rectangular box have 8 or 12 vertices? Explain.
A vertex is a corner; there are four corners on each of two opposite rectangular ends.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Draw one connected, foldable six-face net of a 6 cm by 2 cm by 4 cm cuboid. Label each face with its dimensions.
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.