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 - 11-4 Volumes of Prisms and Cylinders - Practice and Problem-Solving Exercises: 10

Answer

$\approx$ 280.6 $cm^{3}$

Work Step by Step

Find the area of the base of the prism. Each base of the triangular prism is an equilateral triangle. An altitude of the triangle divides it into two 30-60-90 triangles. The height of the triangle is $\sqrt 3$ x the shorter leg, which is 3$\sqrt 3$. B=$\frac{1}{2}$bh B=$\frac{1}{2}$(6)(3$\sqrt 3$) B=9$\sqrt 3$ V=Bh V=9$\sqrt 3$(18) V=162$\sqrt 3$ V=280.5922308
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