Chapter 12, Problem 18CUR

To determine

To find: The total area and volume of square pyramid.

Answer to Problem 18CUR

Thevolume and total area of square pyramid is 400 and 360respectively.

Explanation of Solution

Given information:The base edge of square pyramid is10 and the height is12.

Calculation:

The formula for the area of the square is:

  $\text{area}={\left(\text{side}\right)}^2$

The base of pyramid is in the shape of square. Substitute 10 for side in above formula to find the base area of pyramid.

  $\begin{array}{c}Basearea={\left(10\right)}^2\\ =100\end{array}$

The formula for the volume of square pyramid is:

  $\begin{array}{c}V=\frac{1}{3}\times BA\times h\\ =\frac{1}{3}\times 100\times 12\\ =400\end{array}$

Total Area $\left(TA\right)$ of the pyramid can be calculated as:

  $TA=a^2+a\sqrt{a^2+4h^2}$

Substitute 10for $a$ in above equation.

  $\begin{array}{c}TA={10}^2+10\sqrt{{10}^2+4\times {12}^2}\\ =100+10\sqrt{676}\\ =100+10\times 26\\ =360\end{array}$

Therefore, the volume and total area of square pyramid is 400 and 360 respectively.