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Geometry Level 1

The area of the base of this cone is 42. The volume of this cone is 42. What is its height?

π π 42 π \frac{42}{π} 1 3

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2 solutions

Ben Champion
Feb 15, 2016

V = π r 2 h 3 V=πr^2\frac{h}{3}

A = π r 2 A=πr^2

V = A h 3 V=A\frac{h}{3}

42 = 42 h 3 42=42\frac{h}{3}

h = 3 \boxed{h=3}

Assuming that this is a right circular cone, the volume is given by v = 1 3 A b h v=\dfrac{1}{3}A_b h where A b A_b is the area of the base and h h is the height. Substituting,

42 = 1 3 ( 42 ) ( h ) 42=\dfrac{1}{3}(42)(h)

42 42 cancels out

3 = h \boxed{3=h}

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