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Volume and Surface Area of Spheres and Cones

In this worksheet, students find the volume and surface area of spheres and cones.

'Volume and Surface Area of Spheres and 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 the volume and surface area of spheres and cones.

Here are some useful formulae.

 

Volume = 4  π R3
3
Surface area = 4π  R2
Volume = 1 π R2h
3
Curved surface area = π R l
l = slant length

 

 

Calculate the volume of a sphere with radius 5 cm.

 

(Write your answer to 1 dp and just write the number)

 

Calculate the surface area of a sphere with radius 5 cm.

 

(Write your answer to 1 dp and just write the number)

1 2

 

The radius of Sphere 1 is 5 cm.


Calculate the surface area of a sphere with radius 3 times as big as that of Sphere 1.

 

(Write your answer to 1 dp and just write the number)

1 2

 

The radius of Sphere 1 is 5 cm.


Calculate the volume of a sphere with radius 3 times as big as that of Sphere 1.

 

(Write your answer to 1 dp and just write the number)

Calculate the volume of a sphere with radius 10 cm.

 

(Write your answer to 1 dp and just write the number)

The radius of a sphere is 7 cm.


Calculate its volume.

 

(Write your answer to 1 dp and just write the number)

 

Calculate the volume of a cone with radius 2 cm and height 6 cm.


(Write your answer to 1 dp and just write the number)

 

Calculate the curved surface area of the cone with radius 3 cm and height 4 cm.

 

Hint: Use Pythagoras to calculate the slant length of the cone.

 

(Write your answer to 1 dp and just write the number)

 

Calculate the volume of a cone with radius 3 cm and height 7 cm.


(Write your answer to 1 dp and just write the number)

 

Calculate the curved surface area of the cone with radius 3 cm and height 7 cm.

 

Hint: Use Pythagoras to calculate the slant length of the cone.

 

(Write your answer to 1 dp and just write the number)

  • Question 1

 

Calculate the volume of a sphere with radius 5 cm.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
523.6
EDDIE SAYS
Vol = 4 ÷ 3 × π × 5³
  • Question 2

 

Calculate the surface area of a sphere with radius 5 cm.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
314.2
EDDIE SAYS
Surface area = 4 × π × 5²
  • Question 3
1 2

 

The radius of Sphere 1 is 5 cm.


Calculate the surface area of a sphere with radius 3 times as big as that of Sphere 1.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
2827.4
EDDIE SAYS
Surface area = 4 × π × 15²
  • Question 4
1 2

 

The radius of Sphere 1 is 5 cm.


Calculate the volume of a sphere with radius 3 times as big as that of Sphere 1.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
14137.2
EDDIE SAYS
Vol = 4 ÷ 3 × π × 15³
  • Question 5

Calculate the volume of a sphere with radius 10 cm.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
4188.8
EDDIE SAYS
Vol = 4 ÷ 3 × π × 10³
  • Question 6

The radius of a sphere is 7 cm.


Calculate its volume.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
1436.8
EDDIE SAYS
Vol = 4 ÷ 3 × π × 7³
  • Question 7

 

Calculate the volume of a cone with radius 2 cm and height 6 cm.


(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
25.1
EDDIE SAYS
Vol = 1 ÷ 3 × π × 2² × 6
  • Question 8

 

Calculate the curved surface area of the cone with radius 3 cm and height 4 cm.

 

Hint: Use Pythagoras to calculate the slant length of the cone.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
47.1
EDDIE SAYS
This is a 3, 4, 5 Pythagorean Triad.
Curved Surface Area = π × 3 × 5
  • Question 9

 

Calculate the volume of a cone with radius 3 cm and height 7 cm.


(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
66.0
EDDIE SAYS
Vol = 1 ÷ 3 × π × 3² × 7
  • Question 10

 

Calculate the curved surface area of the cone with radius 3 cm and height 7 cm.

 

Hint: Use Pythagoras to calculate the slant length of the cone.

 

(Write your answer to 1 dp and just write the number)

CORRECT ANSWER
71.8
EDDIE SAYS
Slant length = √(3sup2; + 7sup2;) = √58
Curved Surface Area = π × 3 × √58
---- OR ----

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