Measures and solids · Ages 12–13

Cross-sections worksheet

Part of: 3-D figures

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Measures and solids · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A prism on a 3-sided base is cut parallel to its base. How many sides does the cross-section have?
Answer:
2.A cuboid 3 cm long, 5 cm wide and 11 cm high lies on a table. A plane parallel to the table cuts it. What is the cross-section's area, in cm²?
Answer:
3.A cylinder has base radius 6 cm and height 7 cm. Cut through its axis, the cross-section is a rectangle: cm high, cm wide, with area cm².
Fill in each blank
Answer:
4.A cylinder has base radius 2 cm and height 14 cm. Cut through its axis, the cross-section is a rectangle: cm high, cm wide, with area cm².
Fill in each blank
Answer:
5.A sphere has radius 13 cm. A plane cuts it, and the cross-section is a circle. At most, how many cm across is that circle?
Answer:
6.A sphere has radius 11 cm. A plane cuts it, and the cross-section is a circle. At most, how many cm across is that circle?
Answer:

7.A plane cuts the solid in the picture; the shaded part is the cross-section. What shape is it?
- A
- B
- C
- D
Choose the right picture
Answer:
8.The solid is cut parallel to its base; the shaded part is the cross-section. It is the same shape as the base and the same size.
True or false?
Answer:
9.Wherever a solid is cut parallel to its base, the cross-section is the same 7-sided polygon. What is the solid?
- A. A prism on a 9-sided base
- B. A pyramid on a 7-sided base
- C. A prism on a 7-sided base
- D. A cylinder
Choose the right answer
Answer:
10.An upright plane cuts the solid in the picture; the shaded part is the cross-section. What shape is it?
- A
- B
- C
- D
Choose the right picture
Answer:
11.A plane cuts the solid in the picture; the shaded part is the cross-section. What shape is it?
- A
- B
- C
- D
Choose the right picture
Answer:
12.A plane cuts a cube. Which of these can the cross-section never be?
- A. A circle
- B. A triangle
- C. A pentagon
- D. A hexagon
Choose the right answer
Answer:

13.A wooden cube of side 5 cm is cut parallel to its faces into 1 cm cubes. Pieces may not be stacked to cut together. At least how many cuts does it take?
Working:
Answer:
14.A wooden cuboid is 15 cm long and 4 cm high. Cut in two parallel to its base, its total surface area grows by 120 cm². How wide is it, in cm?
Working:
Answer:
15.A round cake 25 cm across and 11 cm high is cut straight down through its centre into halves. Each cut face is a rectangle cm wide and cm high, and the two together are cm².
Fill in each blank
Working:
Answer:
16.A wooden post, a cylinder 3 cm high with base circumference 9.42 cm, is sawn through its axis into halves. Find the two cut faces' total area (π as 3.14): put the steps in order.
- A. Two cut faces = 2 × 9 = 18
- B. One cut face = 3 × 3 = 9
- C. Diameter = 9.42 ÷ 3.14 = 3
Write the letters in the right order
Working:
Answer:
17.Take π as 3.14. An orange is a sphere of radius 7 cm. Cut it open, the cut is a circle. At most, how long is that circle's circumference, in cm?
Working:
Answer:
18.A loaf is 38 cm long, each end a square of side 9 cm. Cut parallel to the ends into slices 2 cm thick, it makes slices, each cut face cm².
Fill in each blank
Working:
Answer:

Show the answers and working

Cross-sections worksheet: Answers and working

1. 3 sides
Cut parallel to its base, a prism gives a copy of the base: 3 sides.
2. 15 cm²
Parallel to the base, the cut is the base again, 3 cm by 5 cm: 3 × 5 = 15. The height, 11 cm, makes no difference.
3. 7, 12, 84
It is as high as the cylinder, 7 cm, and as wide as the base's diameter, 2 × 6 = 12 cm: area 7 × 12 = 84 cm².
4. 14, 4, 56
It is as high as the cylinder, 14 cm, and as wide as the base's diameter, 2 × 2 = 4 cm: area 14 × 4 = 56 cm².
5. 26 cm
The cut through the centre is the biggest: its radius is the sphere's, 13 cm, so it is 2 × 13 = 26 cm across.
6. 22 cm
The cut through the centre is the biggest: its radius is the sphere's, 11 cm, so it is 2 × 11 = 22 cm across.

7. A
A prism or cylinder cut parallel to its base gives the base again; a pyramid or cone gives the base's shape, smaller near the top; a sphere always gives a circle; a lying triangular prism cut level gives a rectangle.
8. True
Prisms and cylinders (the cube, the cuboid, the cylinder) cut parallel to the base give an exact copy of it; a cone's or pyramid's cut has the base's shape but shrinks towards the apex.
9. C. A prism on a 7-sided base
The same cross-section all the way along marks a prism; 7 sides makes it a prism on a 7-sided base.
10. A
Cut upright: a cube gives a square, a cuboid or cylinder a rectangle, a cone or pyramid through the apex a triangle, a triangular prism a triangle across it or a rectangle along it, a sphere a circle.
11. A
The cross-section has as many sides as faces the plane cuts: a corner cut off cuts 3, a triangle; across all 6 of a cube's faces, a hexagon; through two opposite upright edges, a rectangle; two parallel cuts of different lengths, a trapezium.
12. A. A circle
A cube's faces are flat, so a cut has straight sides and can't be a circle; crossing 3, 4, 5 or 6 faces it has 3, 4, 5 or 6 sides.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 12 cuts
Each direction splits 5 cm into 5 parts with 5 − 1 cuts; three directions: 3 × (5 − 1) = 12.
14. 4 cm
One cut adds two faces matching the base: 2 × 15 × width = 120, so width = 120 ÷ 2 ÷ 15 = 4. The height, 4 cm, plays no part.
15. 25, 11, 550
Cut through the axis, the cut is the diameter wide, 25 cm, and 11 cm high; each half has one: 2 × 25 × 11 = 550.
16. C → B → A
The cut is a rectangle as wide as the diameter and as high as the post: diameter from the circumference, then one face, then double.
17. 43.96 cm
The cut through the centre is biggest, radius 7 cm: 2 × 3.14 × 7 = 43.96.
18. 19, 81
The loaf is a prism: cut parallel to its ends, every slice matches the end, 9 × 9 = 81; slices: 38 ÷ 2 = 19.

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