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The diameter and height of a circular cylinder are 20 feet and 4 feet respectively. What is the volume of water in gallons, if the given cylinder is filled to a height of 3 feet and 6 inches? ( 1 feet $=12$ inches, 1 gallon $=231$ cubic inches)

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567007

576007

586007

587007

answer is A.

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Detailed Solution

We have a cylinder with a base diameter of

20

feet and a height of

4

feet.
We determine the height “

h

" to be

3

feet

6

inches since the cylinder must be filled to a height of

3

feet and

6

inches.
Given that the base's diameter is

20

feet
The radius of the base of the cylinder

= 202 = 10

feet
We now translate the height and radius values from feet to inches.
Since 1 feet is equal to

12

inches

⇒ 10

feet

= 12 × 10

inches

⇒ 10

feet

= 120

inches
Thus, Radius of the base,

r = 120

inches ... (2)
As of right now, the cylinder's height is 3 feet, 6 inches.

⇒ 3 feet = 12 × 3 inches ⇒ 3 feet = 36 inches

So,

3

feet

6

inches will be

= 36 + 6

inches

⇒ 3

feet

6

inches is equal to

42

inches
Height of the cylinder,

h = 42

inches …… (3)
Since we know volume of a cylinder is given by

π r 2 h

Insert the values from equations (2) and (3) in the formula of volume

⇒ V = 227 × 120 × 120 × 42

cubic inches
Remove the same factors from the denominator and numerator.

⇒ V = (22 × 120 × 120 × 6)

cubic inches

⇒ V = 1900800

cubic inches
We employ the conversion of cubic inches into gallons because we need volume in units of gallons. i.e. 1 gallon is equal to

231

cubic inches
Since, 231 cubic inches is equal to one gallon
one cubic inch will be equal to

1231

gallon

⇒ 1900800

cubic inch

= 1231 × 1900800

gallon
Cancel same factors from numerator and denominator

⇒ 1900800

cubic inch

= 576007

gallon
Since Volume of water is

576007

gallon
Hence, Option 1 is correct.
of Linear Equations
of Linear Equations
of Linear Equations

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The diameter and height of a circular cylinder are 20 feet and 4 feet respectively. What is the volume of water in gallons, if the given cylinder is filled to a height of 3 feet and 6 inches? ( 1 feet $=12$ inches, 1 gallon $=231$ cubic inches)

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