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Frustums of Cones

In this worksheet, students find the volumes of frustums of cones.

'Frustums of Cones' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Calculate Surface Areas and Volumes of Spheres, Pyramids, Cones and Composite Solids

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about frustums of cones.

 

Method

20
  5

 

A solid cone has a diameter of 5 cm and a height of 20 cm. 
The top half of the cone is cut off half way up to leave a frustum behind.

(i) the radius of the circle at the top of the frustrum (using proportion) is half the base radius, so here it is 1.25 cm

(ii) the volume of the original cone is 1/3 base area x height, using base radius of 2.5 cm

(iii) the volume of the cone removed is 1/3 base area x height, using base radius of 1.25 cm

(iv) the volume of the frustum is obtained by subtracting these two volumes.

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm.
The top half of the cone is cut off half way up.

Find the radius of the circle at the top of the frustum (use proportion) 

Just write down the number for all answers in this worksheet.

 
cm

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm. 

The top half of the cone is cut off half way up.

Find the volume of the original cone to 3 s.f 
 

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm. 
The top half of the cone is cut off half way up.

Find the volume of the cone removed to 3 s.f. 
 

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm. 
The top half of the cone is cut off half way up.

Find the volume of the frustum to 3 s.f. 
 

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the radius of the circle at the top of the frustum (use proportion)
 
cm

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the volume of the original cone to 3 s.f.
 

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the volume of the cone removed to 3 s.f.    

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the volume of the frustum to 3 s.f.
 

18
  6

 

A solid cone has a diameter of 6 cm and a height of 18 cm. 
The top half of the cone is cut off half way up.

 Find the radius of the circle at the top of the frustum (use proportion)
 
cm

18
  6

 

A solid cone has a diameter of 6 cm and a height of 18 cm. 
The top half of the cone is cut off half way up.

Find the volume of the frustum to 3 s.f.
 
  • Question 1

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm.
The top half of the cone is cut off half way up.

Find the radius of the circle at the top of the frustum (use proportion) 

Just write down the number for all answers in this worksheet.

 
cm
CORRECT ANSWER
1.75
EDDIE SAYS
Half of the base radius 3.5
  • Question 2

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm. 

The top half of the cone is cut off half way up.

Find the volume of the original cone to 3 s.f 
 
CORRECT ANSWER
257
EDDIE SAYS
Vol = 1 ÷ 3 × π × 3.5² × 20
  • Question 3

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm. 
The top half of the cone is cut off half way up.

Find the volume of the cone removed to 3 s.f. 
 
CORRECT ANSWER
32.1
EDDIE SAYS
Vol = 1 ÷ 3 × π × 1.75² × 10
  • Question 4

20
  7

 

A solid cone has a diameter of 7 cm and a height of 20 cm. 
The top half of the cone is cut off half way up.

Find the volume of the frustum to 3 s.f. 
 
CORRECT ANSWER
224
EDDIE SAYS
Subtract the volume of the top cone from the original cone.
  • Question 5

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the radius of the circle at the top of the frustum (use proportion)
 
cm
CORRECT ANSWER
2
EDDIE SAYS
Half of the base radius 4
  • Question 6

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the volume of the original cone to 3 s.f.
 
CORRECT ANSWER
251
EDDIE SAYS
Vol = 1 ÷ 3 × π × 4² × 15
  • Question 7

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the volume of the cone removed to 3 s.f.    
CORRECT ANSWER
31.4
EDDIE SAYS
Vol = 1 ÷ 3 × π × 2² × 7.5
  • Question 8

15
  8

 

A solid cone has a diameter of 8 cm and a height of 15 cm. 
The top half of the cone is cut off half way up.

Find the volume of the frustum to 3 s.f.
 
CORRECT ANSWER
220
EDDIE SAYS
Subtract the volume of the top cone from the original.
  • Question 9

18
  6

 

A solid cone has a diameter of 6 cm and a height of 18 cm. 
The top half of the cone is cut off half way up.

 Find the radius of the circle at the top of the frustum (use proportion)
 
cm
CORRECT ANSWER
1.5
EDDIE SAYS
Half of the base radius 3
  • Question 10

18
  6

 

A solid cone has a diameter of 6 cm and a height of 18 cm. 
The top half of the cone is cut off half way up.

Find the volume of the frustum to 3 s.f.
 
CORRECT ANSWER
148
EDDIE SAYS
Vol of original = 1 ÷ 3 × π × 3² × 18
Vol of top cone = 1 ÷ 3 × π × 1.5² × 9
---- OR ----

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