VOLUME OF A SPHERE WORD PROBLEMS WORKSHEET 

1. Soccer balls come in several different sizes. One of the soccer balls has a diameter of 24 centimeters. What is the volume of this soccer ball ? Round your answer to the nearest tenth. Use the approximate of value of π, that is 3.14. 

2. Jose measures the diameter of a ball as 14 inches. How many cubic inches of air can the ball hold, to the nearest tenth ? Use the approximate of value of π, that is 3.14. 

3. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per minute. If the radius of the ball is 7 feet, how long would it take for the balloon to empty fully ? Round your answer to the nearest minute. Use the approximate of value of π, that is 3.14. 

4. A softball has a volume of 125/6 π cubic inches. Find the radius of the softball.

5. The volume of a solid hemisphere is 29106 cm3. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

6. Calculate the mass of a hollow brass sphere if the inner diameter is 14 cm and thickness is 1mm, and whose density is 17.3 g/ cm³.

7. A solid sphere its perfectly inside of a cube box of side length 10cm. What percentage of the box is empty?

8. A ball of gold has a radius of 9cm. The density of gold is 19.3g/cm³. Work out the mass of the ball.

1. Answer :

Step 1 : 

Because soccer ball is in the shape of sphere, we can use the formula of volume of a sphere to find volume of the soccer ball.  

Write the formula to find volume of a sphere.

V  =  4/3 · πr³ -----(1)

Step 2 : 

To find the volume, we need the radius of the sphere. But, the diameter is given, that is  24 cm. So, find the radius. 

r  =  diameter / 2

r  =  24/2

r  =  12

Step 3 : 

Substitute π ≈  3.14 and r = 12 in (1).

V ≈  4/3 · 3.14 · 12³

Simplify.

V ≈  4/3 · 3.14 · 1728

V ≈  7,234.6

So, the volume of the soccer ball is about 7,234.6 cubic cm. 

2. Answer :

Step 1 : 

To know how much air the ball can hold, we have to find the volume of the ball. 

Because a ball is in the shape of sphere, we can use the formula of volume of a sphere to find volume of a ball.  

Write the formula to find volume of a sphere.

V  =  4/3 · πr³ -----(1)

Step 2 : 

To find the volume, we need the radius of the sphere. But, the diameter is given, that is  14 cm. So, find the radius. 

r  =  diameter / 2

r  =  14/2

r  =  7

Step 3 : 

Substitute π ≈  3.14 and r = 7 in (1).

V ≈  4/3 · 3.14 · 7³

Simplify.

V ≈  4/3 · 3.14 · 343

V ≈  1,436

So, the ball can hold about 1,436 cubic inches.

3. Answer :

Step 1 : 

To know how long it would take for the balloon to empty fully, first we have to find the volume of air in the ballon.

Because the balloon is in the shape of sphere, we can use the formula of volume of a sphere to find volume of air in the balloon. 

Write the formula to find volume of a sphere.

V  =  4/3 · πr³ -----(1)

Step 2 : 

Substitute π ≈  3.14 and r = 7 in (1).

V ≈  4/3 · 3.14 · 7³

Simplify.

V ≈  4/3 · 3.14 · 343

V ≈  1,436

So, the volume of air in the balloon is about 1,436 feet. 

Step 3 : 

Air is leaking from the balloon at the rate of 26 cubic feet per minute.

To know how long it would take for the balloon  to empty 1,426 cubic feet of air, divide 1,426 by 26. 

=  1,426 / 26

=  54.8

  ≈  55

So, it would take about 55 minutes for the balloon to empty fully.

4. Answer :

Volume of sphereical softball = (125/6) π cubic inches.

4/3 · πr³ = (125/6) π

r³ = (125/6) (3/4)

r³ = (125/8) 

r = ∛(125/8)

r = 5/2

r = 2.5 inches

So, the required radius is 2.5 inches.

5. Answer :

Volume of hemisphere = 29106 cm³

Volume of another hemisphere = 2/3 of 29106

= (2/3) x 29106

Volume of another hemisphere = 19404

2/3 · πr³ = 19404

r³ = 19404 (3/2 x 3.14)

= (19404 x 3)/(2 x 3.14)

= 9269.42

r = 21

So, the radius is 21 cm.

6. Answer :

Inner radius (r) = 14/2 ==> 7 cm 

Let R be the outer radius.

Thickness = 1 mm ==> 1/10 ==> 0.1 cm

Thickness = R - r

0.1 = R - 7

0.1 + 7 = R 

R = 7.1 cm

Volume of hollow sphere = 4/3 · π(R³ - r³)

= (4/3) x 3.14 x (7.1³ - 7³)

= (4/3) x 3.14 x (357.91 - 343)

= (4/3) x 3.14 x (14.91)

= 62.42 cm³

Density = Volume of x mass

= 62.42 x 17.3

= 1079.86 grams

Approximately the volume is 1080 grams.

7. Answer :

Volume of cube = a³

a = 10 cm

= 10³

= 1000 cm³

Diameter of sphere = 10 cm

radius = 5 cm

Volume of sphere = 4/3 · πr³

= (4/3) x 3.14 x 5³

= 523.3 cm³

Percentage box which is empty

= [(1000 - 523.3)/1000] x 100%

= (476.7/1000) x 100%

= 47.67%

8. Answer :

Radius of sphere = 9 cm

Volume of sphere = 4/3 · πr³

= 4/3 x 3.14 x 9³

= 3052.08 cm³

Mass = 19.3 g/cm³

Volume = 3052.08 x 19.3

= 58905.144 cm³

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