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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

4. Surface Areas and Volumes of Similar Solids

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Exercise 5 Page 448

When two solids are similar, the ratio of their volumes is equal to the ratio of their corresponding linear measures cubed.

21.3 cubic inches

Practice makes perfect

We know the corresponding side of two similar pyramids but the volume of just one of them.

prisms

We will use the fact that these pyramids are similar to find the volume of the bigger pyramid. When two solids are similar, the ratio of their volumes is equal to the ratio of their corresponding linear measures cubed. Volume of the smaller pyramid/Volume of the bigger pyramid = (Side of the smaller pyramid/Side of the bigger pyramid)^3 We know that the side and the volume of the smaller pyramid are 3 inches and 9 cubic inches, respectively. We also know that the side of the bigger pyramid is 4 inches. If we let V be the volume of the bigger pyramid, we can substitute these values in the equation and solve for V.

Volume of the smaller pyramid/Volume of the bigger pyramid=(Side of the smaller pyramid/Side of the bigger pyramid)^3

SubstituteValues

Substitute values

9/V=(3/4)^3

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Solve for V

(a/b)^m=a^m/b^m

9/V=3^3/4^3

Calculate power

9/V=27/64

LHS * V=RHS* V

9=27/64 * V

MoveRightFacToNum

a/c* b = a* b/c

9=27 * V/64

LHS * 64=RHS* 64

9 * 64=27 * V

Multiply

576=27 V

.LHS /27.=.RHS /27.

576/27=V

Rearrange equation

V=576/27

Calculate quotient

V=21.333333...

Round to 1 decimal place(s)

V ≈ 21.3

The volume of the bigger pyramid is about 21.3 cubic inches.

Subchapter links

Try It p.446-448

Self-Assessment for Concepts & Skills p.448

Self-Assessment for Problem Solving p.449

Review & Refresh p.450