Chapter 1, Problem 22CR

a.

To determine

The formula for height h.

Answer to Problem 22CR

  $h=\frac{3V}{B}$.

Explanation of Solution

Given:

The volume V of a pyramid is given by the formula $V=\frac{1}{3}Bh$ , where B is the area of the base and h is the height.

Calculation:

  $\begin{array}{l}V=\frac{1}{3}Bh\\ \Rightarrow \frac{1}{3}Bh=V\\ \Rightarrow Bh=3V\\ \Rightarrow h=\frac{3V}{B}\end{array}$

Thus, the formula for h is $h=\frac{3V}{B}$

b.

To determine

The height of pyramid.

Answer to Problem 22CR

The height of the pyramid is $18cm$ .

Explanation of Solution

Given:

The area of the base of the pyramid is $B=36c{m}^2$ and volume of the pyramid is $V=216c{m}^3$

Calculation:

  $h=\frac{3V}{B}\mathrm{.....................}(1)$

Putting $B=36c{m}^2$ and $V=216c{m}^3$ in (1),

  $h=\frac{3\times 216}{36}=18$

Thus height of the pyramid is $18cm$ .