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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 54 Page 855

Use the formula for the volume of a pyramid.

240 in^3

Practice makes perfect

We want to find volume of a pyramid.

The volume of a pyramid can be calculated using the following formula. V=1/3BHHere B is the area of the base and H is the height. We are given that H=12inches. We need to find the area of the base, which is a right triangle. Let's recall that the area of a triangle is given by the following formula. B=1/2ah We have the length of a. To find the length of h we will use the Pythagorean Theorem.

Pythagorean Theorem
For a right triangle with legs a and b, and hypotenuse c, a^2+b^2=c^2.

Let's apply what information we have about the base of the pyramid to the formula. 8^2+h^2=17^2 Now we can find the value of h.

8^2+h^2=17^2

Calculate power

64+h^2=289

LHS-64=RHS-64

h^2=225

sqrt(LHS)=sqrt(RHS)

h=15

Let's calculate the area of the base since we now know the value of h.

B=1/2ah

a= 8, h= 15

B=1/2( 8) 15

▼

Simplify right-hand side

Multiply

B=1/2120

MoveRightFacToNumOne

1/b* a = a/b

B=120/2

Calculate quotient

B=60

We have all the values necessary to calculate the volume of the pyramid. Let's substitute these values into the formula and calculate V.

V=1/3Bh

B= 60, H= 12

V=1/3( 60)( 12)

▼

Simplify right-hand side

Multiply

V=1/3720

MoveRightFacToNumOne

1/b* a = a/b

V=720/3

Calculate quotient

V=240

The volume of the pyramid is 240 in^3.

Subchapter links

Exercises p.852-855