Exercise 19 Page 439

Practice makes perfect

a The formula for calculating the volume of a sphere is the product of the cube of the radius, π and 43. We can use it to find the volume of the pinata.

V=4/3π r^3In order to calculate the volume in cubic inches, we first have to rewrite the radius from feet to inches. Since 1 feet equals 12 inches, we can determine the number of inches by multiplying the number of feet by 12. 2(12)=24 inches. The sphere's radius is 24 inches. Now we can calculate the volume of the sphere in cubic inches.

V=4/3π r^3

Substitute

r= 24

V=4/3π( 24)^3

▼

Evaluate right-hand side

CalcPow

Calculate power

V=4/3π(13 824)

MoveRightFacToNum

a/c* b = a* b/c

V=55 296π/3

CalcQuot

Calculate quotient

V=18 423π

Multiply

V=57 905.83579...

\RoundInte

V≈ 57 906

The volume is about 57 906 inches^3.

b In Part A we had to multiply the number of feet by 12 to get it in inches. Therefore, a radius of x feet is equal to a radius of 12x inches. Let's substitute this into the function, which we will use to find the formula for computing the capacities.

V=4/3π r^3

Substitute

r= 12x

V=4/3π( 12x)^3

▼

Evaluate right-hand side

PowProdII

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

V=4/3π(12^3x^3)

MoveRightFacToNum

a/c* b = a* b/c

V=12^3 4x^3 π/3