Shape and space · Ages 10–11
Cross-sections of solids worksheet
Part of: Solid shapes
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Cross-sections of solids worksheet
Shape and space · Ages 10–11
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Choose, or true or false (2 marks each)
1.A cone's base is 17 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It becomes a triangle
- B. The same, 17 cm across
- C. It gets smaller
- D. It gets bigger
Choose the right answer
Answer:
2.The solid in the picture is cut parallel to its base. Which shape is the cut (the cross-section)?
- A
- B
- C
- D
Choose the right picture
Answer:
3.A cone's base is 7 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It gets smaller
- B. It becomes a triangle
- C. The same, 7 cm across
- D. It gets bigger
Choose the right answer
Answer:
4.A cone's base is 10 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It gets bigger
- B. It gets smaller
- C. The same, 10 cm across
- D. It becomes a triangle
Choose the right answer
Answer:
5.A cone's base is 13 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It gets bigger
- B. It gets smaller
- C. It becomes a triangle
- D. The same, 13 cm across
Choose the right answer
Answer:
6.A cone's base is 11 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It becomes a triangle
- B. The same, 11 cm across
- C. It gets smaller
- D. It gets bigger
Choose the right answer
Answer:
7.Which solid always has a circle for a cross-section, however it is cut?
- A
- B
- C
- D
Choose the right picture
Answer:
8.If the solid in the picture is sliced many times parallel to its base, every cross-section is the same size.
True or false?
Answer:
9.A cone's base is 5 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. The same, 5 cm across
- B. It gets smaller
- C. It gets bigger
- D. It becomes a triangle
Choose the right answer
Answer:
10.A cone's base is 14 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It becomes a triangle
- B. It gets smaller
- C. The same, 14 cm across
- D. It gets bigger
Choose the right answer
Answer:
11.A cone's base is 4 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It becomes a triangle
- B. The same, 4 cm across
- C. It gets smaller
- D. It gets bigger
Choose the right answer
Answer:
12.A cone's base is 8 cm across. Cut parallel to the base, what happens to the circle the nearer the cut is to the point?
- A. It gets smaller
- B. It becomes a triangle
- C. The same, 8 cm across
- D. It gets bigger
Choose the right answer
Answer:
Part B: Word problems (4 marks each)
13.A watermelon is roughly a sphere 23 cm across. Cut through its centre, what is the radius of the circular cut, in cm?
Working:
Answer:
14.Ka-yan cuts a cylindrical sausage 6 cm across into 6 slices, parallel to its ends. How many centimetres across is each slice's circle?
Working:
Answer:
15.Ka-yee cuts a cone-shaped wafer, 11 cm tall and 4 cm across, once near its base and once near its point, both parallel to the base. Which cut is bigger?
- A. They are the same
- B. The one near the point
- C. The one near the base
- D. Can't tell without the exact heights
Choose the right answer
Working:
Answer:
16.Ka-lok cuts a cylindrical sausage 3 cm across into 4 slices, parallel to its ends. How many centimetres across is each slice's circle?
Working:
Answer:
17.Chi-keung cuts a cone-shaped wafer, 10 cm tall and 6 cm across, once near its base and once near its point, both parallel to the base. Which cut is bigger?
- A. Can't tell without the exact heights
- B. The one near the point
- C. The one near the base
- D. They are the same
Choose the right answer
Working:
Answer:
18.A watermelon is roughly a sphere 20 cm across. Cut through its centre, what is the radius of the circular cut, in cm?
Working:
Answer:
Show the answers and working
Cross-sections of solids worksheet: Answers and working
Part A: Choose, or true or false
1. C. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
2. A
Look at the solid's base first. Cut parallel to it, how does the cross-section compare with the base?
Cut parallel to the base, the cross-section has the base's shape.
3. A. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
4. B. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
5. B. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
6. C. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
7. A
Take each solid in turn: is there any way to cut it that doesn't give a circle?
Every point of a sphere is the same distance from its centre, so every cross-section is a circle.
8. True
First decide: is the solid the same width all the way up, like a prism or cylinder, or does it narrow to a point, like a pyramid or cone?
Prisms and cylinders (cubes and cuboids too) have every slice the size of the base; pyramids and cones get smaller towards the top.
9. B. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
10. B. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
11. C. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
12. A. It gets smaller
Picture the cone from its base up to its point: how does its width change?
A cone's cross-sections are circles shrinking from the base to a point at the top.
Part B: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 11.5 cm
The cut through the centre is the biggest circle. How does its width compare with the melon's 23 cm, and what part of a diameter is the radius?
A cut through the centre is the biggest, as wide as the sphere, 23 cm: radius 11.5.
14. 6 cm
The sausage is a cylinder. Cut parallel to its ends, is each slice's circle any different in size from an end?
A cylinder's cross-sections parallel to its base match the base: 6 cm, however many slices.
15. C. The one near the base
The wafer is a cone. Think how the slices change size from the base to the point.
A cone's slices shrink from base to point, so the cut near the base is bigger.
16. 3 cm
The sausage is a cylinder. Cut parallel to its ends, is each slice's circle any different in size from an end?
A cylinder's cross-sections parallel to its base match the base: 3 cm, however many slices.
17. C. The one near the base
The wafer is a cone. Think how the slices change size from the base to the point.
A cone's slices shrink from base to point, so the cut near the base is bigger.
18. 10 cm
The cut through the centre is the biggest circle. How does its width compare with the melon's 20 cm, and what part of a diameter is the radius?
A cut through the centre is the biggest, as wide as the sphere, 20 cm: radius 10.
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