Question

A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 3 ft and a radius of 7 ft. The tank will bemade from metal (including its top and bottom). Suppose the total cost of the metal will be $14,946.40. How much will the metal cost per square foot? Use 3.14for π, and do not round your answer.

Answer 1

Solution

Step 1:

Since the metal included both the top and the bottom, hence you will need to find the total surface area of the cylinder.

Step 2

Given data

r = 7ft

h = 3ft

Step 3

$\begin{gathered} Total\text{ surface area = 2}\pi r^2\text{ + 2}\pi rh \\ =\text{ 2}\times\text{3.14}\times7^2\text{ + 2}\times3.14\times7\times3 \\ =\text{ 307.72 + 131.88} \\ =\text{ 439.6 ft}^2 \end{gathered}$

Step 4 :

Divide the total cost by the total surface area to find how much will the metal cost per square foot.

$\begin{gathered} =\text{ }\frac{14946.40}{439.6} \\ =\text{ \ 34/ft}^2\text{ } \end{gathered}$

Final answer

It cost $34 per square foot.