Chapter 1.1, Problem 53E

To determine

To find:The area of the base B of the solid.

Answer to Problem 53E

The area of the base B of the solids is 12 ${\text{in}}^2$ .

Explanation of Solution

Given information:

Volume of cylinder = $84\pi i{n}^3$ and height of cylinder $=7in$ .

Formula Used: Volume of cylinder(V) $=B\cdot h\cdot \pi$ ,

whereB is base areaand h is the height of the cylinder.

Calculations:

Plugging the values v = $84\pi {\text{ in}}^3\text{ and }h=7$ in

V $=B\cdot h\cdot \pi$

  $84\pi =B\cdot 7\cdot \pi$

Switch side

  $B\cdot 7\cdot \pi =84\pi$

Dividing by $7\pi$ on both sides.

  $\frac{B\cdot 7\cdot \pi }{7\pi }=\frac{84\pi }{7\pi }$

Simplify

  $B=12$

Therefore, the base area of cylinder is 12 ${\text{in}}^2$ .