Chapter 10.6, Problem 21E

To determine

To calculate the surface area of pyramid.

Answer to Problem 21E

  $2649$ in²

Explanation of Solution

Given Information: Pyramid Base b = 30 in., Radius r = 15 in. and Height h= 25 in.

Formula Used:

Surface area of square pyramid = $2(b\times s)+b^2$ , Slant Height $s=\sqrt{h^2+r^2}$

Calculation:

Surface area of square pyramid = $2(b\times s)+b^2$

Now, find Slant Height s.

Slant Height of Pyramid $s=\sqrt{h^2+r^2}$

Radius r = 15 in, Height h = 25 in

Now put the value of r and h to find Slant Height of Pyramid

Slant Height of Pyramid $s=\sqrt{{25}^2+{15}^2}$ in

So,

Slant Height of Pyramid $s=\sqrt{625+225}$ in

So,

Slant Height of Pyramid $s=\sqrt{850}$ in

Hence,

Slant Height of Pyramid $s=29.15$ in

Surface area of square pyramid = $2(b\times s)+b^2$

Base b = 30 in. and Slant Height s = 29.15 in

Now put the value of b and s to find Surface area of square pyramid

Surface area of square pyramid = $2(30\times 29.15)+{30}^2$ in²

So,

Surface area of square pyramid = $2\times (874.5)+900$ in²

So,

Surface area of square pyramid = $1749+900$ in²

Hence,

Surface area of square pyramid = $2649$ in²