Chapter 10.6, Problem 28E

To determine

To calculate the surface area of pyramid.

Answer to Problem 28E

  $14444.8$ ft.2

Explanation of Solution

Given Information: Pyramid Base b = 74 ft., Radius $r=\frac{baseb}{2}=\frac{74}{2}=37$ ft. and Height h = 48 ft

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 = 37 ft., Height h = 48 ft.

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

Slant Height of Pyramid $s=\sqrt{{48}^2+{37}^2}$ ft.

So,

Slant Height of Pyramid $s=\sqrt{2304+1369}$ ft.

So,

Slant Height of Pyramid $s=\sqrt{3673}$ ft.

Hence,

Slant Height of Pyramid $s=60.6$ ft.

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

Base b = 74 ft. and Slant Height s = 60.6 ft.

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

Surface area of square pyramid = $2(74\times 60.6)+{74}^2$ ft.2

So,

Surface area of square pyramid = $2\times (4484.4)+5476$ ft.2

So,

Surface area of square pyramid = $8968.8+5476$ ft.2

Hence,

Surface area of square pyramid = $14444.8$ ft.2