Chapter 12.5, Problem 32PPS

To determine

To determine the side length of the base of the pyramid.

Answer to Problem 32PPS

  $l=15\text{ centimeter}$

Explanation of Solution

Given:

Volume of pyramid $=862.5{\text{ centimeter}}^3$

Height of pyramid $=11.5\text{ centimeter}$

Formula used:

Volume of the pyramid $=\frac{lwh}{3}\left[l=\text{length, }w\text{=}\text{width, }h\text{=}\text{height}\right]$

Calculation:

Given, volume of pyramid $=862.5{\text{ centimeter}}^3$

Height of pyramid $=11.5\text{ centimeter}$

Here, the pyramid is square pyramid that is base of the pyramid is square which means,

  $l=w$ [length $=$ width].

To determine the values of sides of the base,

  $\Rightarrow$ Volume of the pyramid $=\frac{l^{2}h}{3}$

  $\Rightarrow$ The values of sides of the base $=\frac{\text{volume}\times 3}{h}$

  $\Rightarrow$ The values of sides of the base $=\frac{862.5\times 3}{11.5}$

  $\Rightarrow$ The values of sides of the base $l^2=225\text{ centimeter}$

  $\Rightarrow$ The values of side of the base $l=\sqrt{225}\text{ centimeter}$

  $\Rightarrow$ The values of side of the base $l=15\text{ centimeter}$

Conclusion:

Therefore, the side length of the base of the pyramid is $l=15\text{ centimeter}$ .