Question

if a cylinder with a height equal to its diameter has a volume of 20 cubic inches. How can you fine the volume of a sphere whose radius is equal to that of a cylinder

Answer 1

you need 2 formulas to do this
volumeof cylinder: pi*r^2*h

volume of sphere: 4/3 * Pi * r^3

you wanna find out the cylinder's height since you have the diameter already. plug in; if height is equal to diameter then radius is half the height, therefore solve in terms of height. r=h/2
V(c)= pir^2h
20= pir^2h
20= pi* (h/2)^2 * h
20= pi * (h^2/4) * h
20= pi * h^3/4
80= pi* h^3
80/pi= h^3
h= cube root of (80/pi)
h= 2.95 inches
r= 1.475 inches

plug this into volume of sphere
V= 4/3 Pi r^3
V= 4/3 pi * (1.475^3)
V= 4/3 pi * (3.21)
V= 4.28 pi
V= 13.446 inches cubed or 13.45 inches cubed