Question

2. A manufacturing company uses cylindrical storage

tanks with a diameter of 40 ft and a height of 80 ft, as
shown below.
a. What is the volume of the storage tanks? Round your answer to the nearest cubic foot.
Show your work.
b. What should the diameter of the storage tank be if the manufacturing company wants
the volume of the storage tank to be 16 times as great as the original volume and the
height remains the same?
Explain your reasoning.
c. The manufacturing company wants to build a rectangular prism-shaped storage tank with
the same height as the original tank. The base of the tank is 30 feet long and 40 feet
wide. Which storage tank will provide the most volume?
Explain your reasoning.

Answer 1

a_ 100,531 ft3

b_ 160 ft

c_The cylindrical storage will provide the most volume

Explanation:

Hi, to answer this question we have to apply the next formula:

A) Volume of a cylinder (V) : π x radius ² x height

Since

Diameter = 2r

Replacing with the value given:

40/2 =r

20ft=r

Back with the volume formula, replacing with the values given and solving for v (Volume)

V = π x 20 ² x 80

V = 100,531 ft3

b) we have to apply the next formula and solve for r:

Vx16 = π x r ² x 80

100,531 x16 = π x r ² x 80

1608495 / π 80 = r^2

6400 = r^2

√6400 =r

80 = r

Since:

Diameter = 2r

D = 2 (80)

D = 160 ft

c) We have to apply the next formula:

Volume of a rectangular prism: base x width x height

V = 30x40x80

V = 96,000ft3

Comparing it with the original tank's volume:

V = 100,531 ft3 >96,000ft3

The cylindrical storage will provide the most volume

Feel free to ask for more if needed or if you did not understand something