Chapter 1, Problem 39SGR

To determine

To find the surface area and volume of each solid

Answer to Problem 39SGR

Volume of the pyramid is $384i{n}^3$

Surface area is $384i{n}^2$

Explanation of Solution

Given information:

Side of square pyramid= $12in$

Height of square pyramid= $8in$

Formula:

Surface area= $a^2+2a\sqrt{\frac{a^2}{4}+h^2}$

Volume= $\frac{1}{3}{a}^{2}h$

Calculation:

Substituting values,

Surface area= ${(12)}^2+2(12)\sqrt{\frac{{(12)}^2}{4}+{(8)}^2}$

Solving,

Surface area= $144+24\sqrt{\frac{144}{4}+64}$

So,

surface area= $144+24\sqrt{36+64}$

And,

Surface area= $144+24(10)$

Hence, surface area is $384i{n}^2$

Now,

Volume= $\frac{1}{3}{(12)}^2(8)$

Solving,

Volume= $(12)(4)(8)$

Multiplying,

Volume= $(12)(32)$

Hence, volume of the pyramid is $384i{n}^3$