Exercise 5 Page 653

We are asked to find the volume of a softball knowing that the volume of a baseball is about 12.8 cubic inches. To do so, let's start by recalling the relationship between the volumes of similar solids.

Volume of Similar Solids

If Solid X is similar to Solid Y by a scale factor, then the volume of X is equal to the volume of Y times the cube of the scale factor.

We are given that the scale factor between the given solids is 1.31. Note that the scale factor is greater than 1. 1.3/1 = 1.3 > 1 This means that the dimensions of the larger solid are larger by a scale factor of 1.3 than the dimensions of the smaller solid. Since the softball is larger than the baseball, we will multiply the volume of a baseball by 1.3 raised to the third power, we will get the volume of a softball. 12.8 * ( 1.3 )^3 = x Note that we got an equation that will help us to find the volume of a softball. Let's solve the equation for x!

12.8 * ( 1.3 )^3 = x

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Solve for x

RearrangeEqn

Rearrange equation

x=12.8 * ( 1.3 )^3

CalcPow

Calculate power

x=12.8 * 2.197

Multiply

Multiply

x= 28.1216

RoundDec

Round to 1 decimal place(s)

x ≈ 28.1

Therefore, x≈ 28.1 is a solution to the equation. This means that the volume of a softball is about 28.1 cubic inches.