Geometry: Common Core (15th Edition)

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

Chapter 11 - Surface Area and Volume - 11-5 Volumes of Pyramids and Cones - Practice and Problem-Solving Exercises - Page 730: 14


$562.9 \ ft^3$

Work Step by Step

Apply the Pythagorean formula to determine the height of the pyramid. $h^2=l^2-(\dfrac{r}{2})^2 \implies h^2=(15)^2 -(5.5)^2\implies h=13.95 \ m$ The volume of a square pyramid is: $Volume =\dfrac{1}{3} \times b\times h=\dfrac{1}{3} \times S^2 \times h$ Plug the values of $S$ and $h$ into the formula to obtain: $Volume=\dfrac{1}{3} \times (11)^2 \times (13.95)\\ =\dfrac{1}{3} \times 121 \times 13.95 \\=562.9 \ ft^3$
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