Exercise 4 Page 656

We are given a triangular pyramid with a volume of 48 cubic inches. One of the base's edges is 9 inches and the height falling on that edge is 4 inches. We want to find the height of this pyramid. Let's first recall the formula for the volume of a pyramid. V=1/3BhHere, B is the area of the base, and h is the height of the pyramid. Since the base is a triangle, the base's area B is half the product of the base edge and the base's height. Let's find this area! B = 1/2( 9)( 4) = 18 The base's area is 18 square inches. Our pyramid has a volume of 48 cubic inches. Let's substitute this values into the formula for the volume of a pyramid. That way, we will get an equation for h. Then, let's solve this equation!

V=1/3Bh

SubstituteII

V= 48, B= 18

48=1/3( 18)h

MultEqn

LHS * 3=RHS* 3

3 * 48 = 18h

Multiply

Multiply

144 = 18h

DivEqn

.LHS /18.=.RHS /18.

144/18 = h

CalcQuot

Calculate quotient

8 = h

RearrangeEqn

Rearrange equation

h = 8

The height is 8 inches.