College algebra

Question

the volume of a 6-in. tall cone varies directly as the square of the radius, the volume is 14.1 cubic inches when the radius is 1.5 in. find the volume when the radius is 3 in.

Answer 1

V=(1/3)∏r²h

V=(1/3)∏(2r)²h

V=(1/3)∏4r²h

if the radius is doubled the volume is quadrupled

therefore 4*14.1=56.4 cubic inches

V=(1/3)(∏)(1.5)²(6)

V=2*∏*2.25

V=4.5*∏

V=4.5*3.14159

V=14.137 cubic inches

V=(1/3)(∏)(3²)(6)

V=2*∏*9

V=18*∏

V=18*3.14159

V=56.548 cubic inches which is slightly different because of the 14.137 compared to 14.1