Chapter 12, Problem 1E

To determine

To find: The volume of the solid with the given altitude.

Answer to Problem 1E

Thevolume of the solid is 22 cubic units.

Explanation of Solution

Given information:

The given solid is oblique pyramid with the height $11$ and the base is right triangle with the sides, $3,4,5$ . Here largest number is the hypotenuse of the triangle. Let the sides of the triangle be,

  $x=3$ , $y=4$ and $z=5$

Calculation:

The formula to calculate the base area of the triangle is,

  $\text{Base area}=\frac{1}{2}\times xy$

Where,

• $x,y$are the legs of the triangle other than hypotenuse.

Substitute $3$ for $x$ and $4$ for $y$ in the above equation.

  $\begin{array}{c}\text{Base area}=\frac{1}{2}\times xy\\ =\frac{1}{2}\times 3\times 4\\ =6\text{square}\text{units}\end{array}$

The formula to calculate the volume of the pyramid is,

  $\text{Volume}=\frac{1}{3}\times \text{Base}\text{area}\times h$

Where,

• $h$ is the height of the pyramid.

Substitute $11$ for $h$ in the above equation.

  $\begin{array}{c}\text{Volume}=\frac{1}{3}\times \text{Base}\text{area}\times h\\ =\frac{1}{3}\times 6\times 11\\ =22\text{cubic}\text{units}\end{array}$

Therefore, the volume of the solid is 22 cubic units.