Frustums of Cones
• Introduction

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.

• 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
• 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
• 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.
• 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.
• 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
• 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.
• 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.
• 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.
• 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
• Question 10