Exercise 6 Page 657

We are given a triangular pyramid with a volume of 270 cubic inches. One of the base's edges is 15 centimeters and the height falling on that edge is 4 centimeters. 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( 15)( 4) = 30 The base's area is 30 square centimeters. Our pyramid has a volume of 270 cubic centimeters. 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= 270, B= 30

270=1/3( 30)h

MultEqn

LHS * 3=RHS* 3

3 * 270 = 30h

Multiply

Multiply

810 = 30h

DivEqn

.LHS /30.=.RHS /30.

810/30 = h

CalcQuot

Calculate quotient

27 = h

RearrangeEqn

Rearrange equation

h = 27

The height is 27 centimeters.