McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Volumes of Pyramids and Cones
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Exercise 32 Page 846

Use the formula for the volume of a pyramid.

15 cm

Practice makes perfect

The volume of a pyramid can be calculated using a known formula. In this formula B is the base area, and h is the height of a pyramid. V=1/3Bh In our exercise the base of the pyramid is a square. Therefore, the base area will be equal to the squared length of the side length of a base, let's call it s. B= s^2 Let's substitute it for B into the volume formula. V=1/3 s^2h We are given that the height is 11.5cm and the volume is 862.5cm. Let's substitute these values into the formula and solve the equation for s. Notice that, since s represents the side length, we will consider only a positive case when taking a square root of s^2.

V=1/3s^2h
862.5=1/3s^2( 11.5)
â–¼
Solve for s
75=1/3s^2
75=s^2/3
225=s^2
15=s
s=15

The side length of the base is 15 cm.