Chapter 12.5, Problem 1CYU

To determine

To find the volume of the given triangular pyramid.

Answer to Problem 1CYU

  $V=75$ cubic inches

Explanation of Solution

Given:

  

Height ( $h$ ) $=10$ inches

Right angled triangular base:

Height $=9$ inches

Base $=5$ inches

Formula used:

Volume of pyramid, $V=\frac{1}{3}Bh$

where $B$ is the area of the base and $h$ is the height of the pyramid.

Area of a triangle $=\frac{1}{2}\times Base\times Height$

Calculation:

Since the given pyramid is a Right angled triangular pyramid, so it has a right angled triangular base.

So, area of the base, $B=\frac{1}{2}\times Base\times Height$

  $\Rightarrow B=\frac{1}{2}\times 5\times 9$

  $\Rightarrow B=22.5$ square inches.

Now for the volume ( $V$ ) of the pyramid,

  $V=\frac{1}{3}Bh$

Now put the values of $B=22.5$ and $h=10$ ,

  $\Rightarrow \frac{1}{3}\times 22.5\times 10$

  $\Rightarrow \frac{225}{3}$

  $\Rightarrow V=75$ cubic inches

Conclusion:

Therefore, the volume of the given triangular pyramid is $75$ cubic inches.