**Finding the volume of a cylinder in a real world context :**

Finding volumes of cylinders is similar to finding volumes of prisms. We can find the volume V of both a prism and a cylinder by multiplying the height by the area of the base.

Let the area of the base of a cylinder be B and the height of the cylinder be h. Write a formula for the cylinder’s volume V.

V = Bh

The base of a cylinder is a circle, so for a cylinder,

B = ∏r**²**

Then, we have

**V = ∏r²h **cubic units

**Example 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 ∏, that is 3.14 and round your answer to the nearest tenth if necessary.

**Solution : **

**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 = ∏r**²**h 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

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

Let us look at the next example on "Finding the volume of a cylinder in a real world context"

**Example 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.

**Solution : **

**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 = ∏r**²**h 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 :**

Plug ∏ ≈ 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

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

Let us look at the next example on "Finding the volume of a cylinder in a real world context"

**Example 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 ?

**Solution : **

**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 = ∏r**²**h 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 :**

Plug ∏ ≈ 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.

Let us look at the next example on "Finding the volume of a cylinder in a real world context"

**Example 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.

**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 = 1/2 · ∏r**²**h 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 :**

Plug ∏ ≈ 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

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

After having gone through the stuff given above, we hope that the students would have understood "Finding the volume of a cylinder in a real world context".

Apart from the stuff given above, if you want to know more about "Finding the volume of a cylinder in a real world context", please click here

Apart from the stuff given on "Finding the volume of a cylinder in a real world context", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**