VOLUME OF A CONE WORD PROBLEMS WORKSHEET

1. The height and diameter of a cone-shaped storage tank are 9 feet and 14 feet respectively. Find the volume of liquid the tank can hold. Round your answer to the integer, if necessary. Use the approximate of value of π, that is 3.14. 

2. A silo is shaped like a cone and contains wheat. The radius is 10 feet and the height is 15 feet. If the silo can release wheat from its bottom at the rate of 25 cubic feet per minute, how long would it take for the silo to empty fully ? Round your answer to the nearest minute. Use the approximate of value of π, that is 3.14. 

3. An artist makes a cone shapes sculpture for an exhibit. If the sculpture is 7 feet tall and has a base with the circumference of 24.492 feet, what is the volume of the sculpture ?

4. A cone has a radius 3 and height 11

a)  Suppose the radius is increased by 4 times its original measure. How many times greater is the volume of the larger cone than the smaller cone ?

b)  How would the volume of the cone change if the radius were divided by four ?

5. Compare the volumes of two cones. One has a radius of 5 feet and slant height of 13 feet. The other cone has the height of 5 feet and a slant height of 13 feet.

a) Which cone has the greater volume ?

b) What is the volume of the larger cone in terms of π

1. Answer :

Step 1 :

Because the tank is in the shape of cone, we can use the formula of volume of a cone to find volume of water the tank can hold.

Write the formula to find volume of a cone.

V  =  1/3 · πr²h -----(1)

Step 2 :

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

r  =  diameter/2

r  =  14/2

r  =  7

Step 3 :

Substitute π ≈ 3.14, r = 7 and h = 9 in (1).

V  ≈  1/3 · 3.14 · 7² · 9

Simplify.

V  ≈  1/3 · 3.14 · 49 · 9

V  ≈  461.58

Round it to the nearest integer.

V  ≈  462

So, the volume of the clay is about 462 cubic inches.

2. Answer :

Step 1 :

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

Because the silo is in the shape of cone, we can use the formula of volume of a cone to find volume of wheat the tank can hold.

Write the formula to find volume of a cone.

V = 1/3 · πr²h -----(1)

Step 2 :

Substitute π ≈ 3.14, r = 10 and h = 15 in (1).

V ≈ 1/3 · 3.14 · 10² · 15

Simplify.

V ≈ 1/3 · 3.14 · 100 · 15

V ≈ 1,570

So, the volume of wheat in the silo is about 1,570 feet.

Step 3 :

Silo can release wheat from its bottom at the rate of 25 cubic feet per minute.

To know how long it would take for the silo to empty 1,570 cubic feet of wheat, divide 1,570 by 25.

= 1,570 / 25

= 62.8

  ≈ 63

So, it would take about 63 minutes for the silo to empty fully.

3. Answer :

Height of sculpture = 7 feet

Circumference of base = 24492 feet

2 π r = 24492

2 x 22/7 x r = 24.492

r = (24.492 x 7)/44

r = 3.89

The radius is approximately 3.9 feet.

Volume of cone = 1/3 · πr²h 

= (1/3) x 3.14 x 3.9² x 7

= 111.43 cubic feet

4. Answer :

Radius = 3 feet and height = 11 feet

New radius = 4(3) ==> 12 feet

a)

Volume of old cone =  1/3 · πr²h 

= (1/3) x 3.14 x 3²x 11

= 103.62

Volume of new cone =  1/3 · πr²h

= (1/3) x 3.14 x 12²x 11

= 1657.92

Volume of new cone / volume of old cone

= 1657.92 / 103.62

= 16

Volume of the new cone is 16 times of volume of smaller cone.

New radius = 3/4 feet

b)

Volume of old cone =  1/3 · πr²h 

= (1/3) x 3.14 x 3²x 11

= 103.62

Volume of new cone =  1/3 · πr²h

= (1/3) x 3.14 x (3/4)²x 11

= 6.47

Change in volume = 103.62/6.47

= 16.01

The new cone will become 16 times smaller than the old cone.

5. Answer :

The first cone :

Radius (r) = 5 feet

Slant height (l) = 13 feet 

h = √l² - r²

h = √13² - 5²

= √(169 - 25)

= √144

h = 12 feet

Volume of new cone =  1/3 · πr²h

= (1/3) x πx 5²x 12

= 100π cubic feet

The second cone :

Radius (r) = ?

Slant height (l) = 13 feet 

height (h) = 5

r = √l² - h²

r = √13² - 5²

= √(169 - 25)

= √144

r = 12 feet

Volume of new cone =  1/3 · πr²h

= (1/3) x π x 12²x 5

= 240 π cubic feet

a) The second cone has larger volume

b) The volume of the larger cone is 240 π cubic feet.

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