Word Problem Exercises: Volume of Right Circular Cylinders

To work problems of this type, we will use the following two formulas:

the volume of a cylinder

V = Bh

the area of the base is

B =

In these formulas,

• h is the height of the cylinder,
• B is the area of the base of the cylinder,
• r is the radius of the cylinder.

To begin our investigation, we will look at two examples.

1. Farmer Jones owns a citrus tree farm in Florida. During some parts of the year the amount of rain in Florida is not sufficient to maintain maximum growth of citrus so farmer Jones is going to buy a water tank. Find how much water it will hold if it is a right circular cylinder with a height of 10 feet and a radius of radius of 5 feet.

Solution:

By substitution,

V = r2h
V = (5)2(10)
V = (25)(10)
V = 250 ft3

If we approximate the value of  = 3.14 then

V =  785 ft3

1. A soup can has a diameter of 10 cm and a height of 15 cm. What is the volume of the soup in the can if 0.5 cm of space is left at the top of the can to allow for expansion?

Solution:

Step 1: Find the area of the base.

The radius of the bottom of the can equals 5 cm since it is half of the diameter (10 cm).

By substitution,

B = r2
B = (5)2
B = (25)
B = 25 cm2

If we approximate the value of  = 3.14 then

B = 78.5 cm2

Step 2: Find the height of the soup in the can.

The can is 15 cm tall but 0.5 cm of space is to be left at the top of the can to allow for expansion,

h = 15 cm - 0.5 cm = 14.5 cm

Step 3: Find the volume of soup.

By substitution,

V = Bh
V = (78.5)(14.5)
V = 1138.25 cm3

General Questions
 Farmer Brown is buying a new water tank for his farm because he needs more water for his crops. His current tank is a right circular cylinder that is 5 meters high and 6 meters across. At the store, he is given a choice of two tanks that he could purchase:   the first one has twice the height of his current tank but keeps the same width. the second one has twice the width of his current tank but keeps the same height.   If both tanks cost the same amount of money, what is the greater volume of water the two tanks could hold?
 1 141.3 m 282.6 m 565.2 m 2260.8 m

 There are 24 cans of soda and they are arranged in 4 rows of 6. Each can has a radius of 4 cm and a height of 15 cm. These cans are to be packed snuggly into a case with no extra space on the top, bottom, or sides. Calculate how much empty space will not be occupied by a can in the box.
 2 23,040 cm3 754 cm3 18,096 cm3 4,944 cm3

S Bay
K Holland

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