VOLUME OF CYLINDER WORD PROBLEMS WORKSHEET

1. The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank. Use the approximate of value of π, that is 3.14 and round your answer to the nearest tenth if necessary.

2. A standard-size bass drum has a diameter of 22 inches  and is 18 inches deep. Find the volume of this drum. Use the approximate of value of  ∏, that is 3.14 and round your answer to the nearest tenth if necessary.

3. A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile of a pipeline that has an inside diameter of 6 inches and is completely filled with oil ? How much is “1 mile” of oil in this pipeline worth at a price of $100 per barrel ?

4. A pan for baking French bread is shaped like half a cylinder as shown in the figure. Find the volume of uncooked dough that would fill this pan. Use the approximate of value of  ∏, that is 3.14 and round your answer to the nearest tenth if necessary.

1. Answer :

Step 1 : 

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

V  =  πr²h cubic units

Step 2 : 

Substitute the given measures. 

V  ≈  3.14 · 18.8² · 24

(Here deep 24 feet is considered as height)

Simplify.

V  ≈  3.14 · 353.44 · 24

V  ≈  26635.2

So, the volume of the tank is about 26635.2 cubic feet.

2. Answer :

Step 1 : 

Usually the bass drum would be in the shape of cylinder. So, we can use the formula of volume of a cylinder, to find volume of the bass drum.

V  =  πr²h cubic units -----(1)

Step 2 : 

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 22 in. So, find the radius. 

r  =  diameter / 2

r  =  22/2

r  =  11

Step 3 :

Substitute π  ≈  3.14, r = 11 and h = 18 in (1).

V ≈  3.14 · 11² · 18

(Here deep 18 inches is considered as height)

Simplify.

V  ≈  3.14 · 121 · 18

V  ≈  6838.9

So, the volume of the bass drum is about 6838.9 cubic inches.

3. Answer :

Step 1 : 

Usually the pipe line would be in the shape of cylinder. So, we can use the formula of volume of a cylinder to find volume of the crude oil in the pipe line. 

V  =  πr²h cubic units -----(1)

Step 2 : 

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 6 in. So, find the radius. 

r  =  diameter / 2

r  =  6/2

r  =  3 inches

Step 3 :

Convert the inches into feet by multiplying 1/12.

Because, 

1 inch  =  1/12 feet

So, we have 

r  =  3 x 1/12 feet

r  =  1/4 feet

Step 4 :

Convert the length of the pipeline from miles to feet.

1 mile  =  5280 feet

So, we have 

length  =  1 mile

length  =  1 x 5280 feet

length  =  5280 feet

Step 5 :

Substitute π  ≈  3.14, r = 1/4 and h = 5280 in (1).

V  ≈  3.14 · (1/4)² · 5280

(Here , the length 5280 feet is considered as height)

Simplify.

V  ≈  3.14 · (1/16) · 5280

V  ≈  1036.2 cubic feet

Step 6 :

To find how many barrels of oil are contained in 1 mile of a pipeline, divide the volume of crude oil in the pipeline (1036.2 cu.ft) by 5.61.

Because a barrel of crude oil contains about 5.61 cubic feet of oil.

So, number of barrels of oil are contained in 1 mile of a pipeline is 

=  1036.2 / 5.61

=  184.7

There are about 184.7 barrels of oil are contained in 1 mile of a pipeline.

Step 7 :

Find the worth of “1 mile” of oil in the pipeline at a price of $100 per barrel.

No. of barrels of oil in 1 mile of a pipeline  =  184.7  

So, the worth of “1 mile” of oil in the pipeline is 

=  $100 x 184.7

=  $18,470

The worth of “1 mile” of oil in the pipeline at a price of $100 per barrel is about $18,470.

4. Answer :

Solution : 

Step 1 : 

Because the pan is shaped like half a cylinder, we can use the formula of volume of a cylinder to find volume of uncooked dough that would fill this pan

V  =  πr²h cubic units -----(1)

(Because the pan is shaped like half a cylinder, 1/2 is multiplied by the formula of volume of a cylinder)

Step 2 : 

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 3.5 in. So, find the radius. 

r  =  diameter / 2

r  =  3.5/2

r  =  1.75

Step 3 :

Substitute π ≈ 3.14, r = 1.75 and h = 12 in (1).

V ≈  1/2 · 3.14 · 1.75² · 12

Simplify.

V  ≈  1/2 · 3.14 · 3.0625 · 12

V  ≈  57.7

So, the volume of uncooked dough that would fill the pan is about 57.7 cu.inches.

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