MUVA
Answered

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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

Sagot :

iGreen
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
[tex]The\ volume\ of\ a\ cone:V=\frac{1}{3}\pi r^2 H=\frac{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\\\\\frac{1}{3}A_b\cdot7=35\\\\\frac{7}{3}A_b=35\ \ \ \ |divide\ both\ sides\ by\ \frac{7}{3}\to multiply\ both\ sides\ by\ \frac{3}{7}\\\\A_b=\frac{35}{1}\cdot\frac{3}{7}=\frac{5}{1}\cdot\frac{3}{1}=5\cdot3=\boxed{15\ (ft^2)}[/tex]
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