Question

The volume of a cone is 35 ft3 and the cone’s height is 7 ft.

What is the area of the base of the cone?

_________ ft2

Answer 1

`The\ volume\ of\ a\ cone:V=(1)/(3)\pi r^2 H=(1)/(3)A_bH\\\\r-the\ radius\ \\H-the\ height\ of\ the\ cone\\A_b-area\ of\ the\ base\\----------------------\\\\V=35\ ft^3;\ H=7\ ft\\\\therefore\\\\(1)/(3)A_b\cdot7=35\\\\(7)/(3)A_b=35\ \ \ \ |divide\ both\ sides\ by\ (7)/(3)\to multiply\ both\ sides\ by\ (3)/(7)\\\\A_b=(35)/(1)\cdot(3)/(7)=(5)/(1)\cdot(3)/(1)=5\cdot3=\boxed{15\ (ft^2)}`

Answer 2

Formula:

V = 1/3 * b * h

Plug in what we know:

35 = 1/3 * b * 7

Multiply 7 * 1/3:

35 = 2 1/3 * b

Multiply:

35 = 2 1/3b

Divide 2 1/3 to both sides:

b = 15