Exercise 3 Page 653

This exercise is asking us to find the volume of the table. Because we are told the tabletop is circular, we will need to find the volume of a cylinder. Let's first recall the formula for the volume of a cylinder with a circular base. Volume= π r^2 h We are told that the diameter is 6 feet and the depth, or height, is 6 inches. Let's start by finding the radius of the circle. Radius= 1/2 * Diameter ⇕ Radius= 1/2 * 6 feet= 3 feet The radius of the circle is 3 feet. The radius and height must be in the same units before we substitute them into the volume of a circle. We are asked to put our answer in cubic feet, so we must convert the height from inches to feet. Converting between inches and feet will involve using a conversion factor. 1 foot/12 inches Multiplying 6 inches by this conversion factor will convert it to feet.

6 inches * 1 foot/12 inches

CrossCommonFac

Cross out common factors

6 inches * 1 foot/12 inches

MoveLeftFacToNumOne

a* 1/b= a/b

6 feet/12

SimpQuot

Simplify quotient

0.5 feet

We now have a radius of 3 feet and height of 0.5 feet. Finally, we can substitute these values into the formula for volume to find out how much concrete is needed.

Volume= π r^2 h

SubstituteII

r= 3 ft, h= 0.5 ft

Volume= π (3 ft)^2 (0.5 ft)

CalcPow

Calculate power

Volume= π * 9 ft^2 * 0.5 ft

Multiply

Multiply

Volume= 4.5 π ft^3

UseCalc

Use a calculator

Volume ≈ 14 ft^3

Mr. Washington will need about 14 cubic feet of concrete to make the top of the table.