Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises - Page 496: 43

Answer

a. $V=64s^3$. b. $ V=48(\pi) s^2$. c. $V=64s^3-48(\pi) s^2$. d. $V=16s^2(4s-3\pi)$. e. $V=182088\;in.^3$.

Work Step by Step

The given values are $a=4s$. $h=48\;in.$. $r=s$. a. Formula for the volume of the cube. $\Rightarrow V_1=a^3$ Substitute the value of $a$. $\Rightarrow V_1=(4s)^3$ Simplify. $\Rightarrow V_1=64s^3$. b. Formula for the volume of the cylinder. $\Rightarrow V_2=\pi r^2h$ Substitute the value of $h$ and $r$. $\Rightarrow V_2=\pi (s)^2(48)$ Simplify. $\Rightarrow V_2=48(\pi) s^2$. c. Metal left. $V=V_1-V_2$ Substitute the values of volumes. $V=64s^3-48(\pi) s^2$. d. Factor out common terms. $V=16s^2(4s-3\pi)$. e. Substitute the value of $s=15\;in.$ and $\pi=3.14$. $V=16(15)^2(4(15)-3(3.14))$. Use a calculator and simplify. $V=182088\;in.^3$.
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