Write a rule for W. find W(5) in terms of x

Question

the function V(x)= 4/3 pi x^3 represents the volume in cubic inches of a sphere. the function W(x)=V(36x) represents the volume in cubic inches of the sphere. when x is measured in feet.Write a rule for W. find W(5) in terms of x

Answer 1

1 foot = 12 inches

1 square foot = 12^2 = 144 in^2

1 ft^3 = 12^3= 1728 in^3

V(x) = (4/3)pi(r^3) where x is measured in inches, V is measured in cubic inches

5 feet = 5(12) = 60 inches

V(60) = (4/3)pi(60^3) = (4/3)pi(216,000)= 4pi(71200) = 288,800pi in^3

W(5 feet) = (4/3)pi(5^3) = (4/3)pi(125) = 500pi/3 ft^3

V(60)/W(5) = 288,800pi/500pi/3 = 2888/5/3 =

1732.8W(5) = V(60)

W(5) = V(60)/1732.8

W(5) =288800pi/1732.8 = 166.666...pi = 500pi/3

W(5) = V(60) = V(12(5)) = V(12x)

W(x) =V(12x), Not V(36x)