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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

4. Volumes of Prisms and Cylinders

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Exercise 11 Page 721

Use the formulas for the area of a triangle and volume of a prism.

22.5ft^3

Practice makes perfect

We are given the following triangular prism, and we want to find its volume.

The volume of a prism can be calculated using the following formula. V=Bh Where B is the area of the base and h is the height of the prism. Note that the base of the prism is a right triangle, so we can calculate its area using the formula for area of a triangle.

B=1/2bh

b= 3, h= 3

B=1/2( 3)( 3)

▼

Evaluate right-hand side

Multiply

B=1/2(9)

MoveRightFacToNumOne

1/b* a = a/b

B=9/2

The area of the base B is 92ft^2, and we are given that the height equals 5ft. Let's substitute these values into the formula and solve for V.

V=Bh

B= 9/2, h= 5

V=( 9/2)( 5)

MoveRightFacToNum

a/c* b = a* b/c

V=45/2

Calculate quotient

V=22.5

Therefore, the volume of the prism is 22.5ft^3.

Subchapter links

Lesson Check p.721

Practice and Problem-Solving Exercises p.721-724

Standardized Test Prep p.724

Mixed Review p.724