Frustums of Cones
Preview only Sign up to use worksheet Signup now
  • Introduction
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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
PREVIEW ONLY. SIGN UP TO USE WORKSHEET.

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.
 
Progress