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 - Page 78: 25


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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.