Chapter 1.1, Problem 55E

To determine

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

Answer to Problem 55E

The area of the base B of the cone = $9{\text{ m}}^2.$

Explanation of Solution

Given information:

Volume of cone $V=15\pi {\text{ m}}^3$ and

height of cone $h=5\text{ m}$ .

Formula Used: Formula of volume of cone $V=\frac{1}{3}B\times h.$

WhereB is base areaandh is height of cuboid.

Calculations:

Plugging $V=15\pi {\text{ m}}^3\text{ and}$

  $h=5\text{ m}$

  $V=\frac{1}{3}B\times h.$

  $15=\frac{1}{3}\times B\times 5$

Switch side

  $\frac{1}{3}\times B\times 5=15$

Multiply by $\frac{3}{5}$ on both sides.

  $\frac{1}{3}\times B\times 5\times \frac{3}{5}=15\times \frac{3}{5}$

Simplify

  $B=9$

Therefore, the base area of cone is $9{\text{ m}}^2.$