Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 1 - Tools of Geometry - Common Core Cumulative Standards Review - Selected Response: 25

Answer

a) $54\pi\ cm^2$ b) no

Work Step by Step

The area of the bottom of one can is given. 6 cans are to be included. Multiply the area of a single can by 6 to find the total. $A=6(9\pi)\ cm^2=54\pi\ cm^2$ The diameter of the can is the widest point. The length of the box needs to accommodate 3 cans. The height needs to accommodate 2 cans.Find the diameter of the can to compute the minimum length and height of the box. Use the formula for the area of a circle to find the radius of the can. $A=\pi r^2$ substitute $9\pi\ cm^2=\pi r^2$ divide each side by $\pi$ $9\pi\ cm^2\div\pi=\pi r^2\div\pi$ $9\ cm^2=r^2$ take the square root of each side $\sqrt{9\ cm^2}=\sqrt{r^2}$ $3\ cm=r$ The diameter of a circle is twice its radius. $d=2r=2(3\ cm)=6\ cm$ The minimum length of the box, in order to accommodate 3 cans, is $3d=3(6\ cm)=18\ cm$ The minimum height of the box, in order to accommodate 2 cans, is $2d=2(6\ cm)=12\ cm$ A box with a length of 16 cm is not large enough, since 18 cm is required.
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