# Frustums of Cones

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

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Difficulty level:

### 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
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
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.
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.
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
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.
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.
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.
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
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.