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As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm. How many cubic centimeters are in the volume of the cone?
JMAP geometry math cone
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As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm.

How many cubic centimeters are in the volume of the cone?

1) 12.5π

2) 13.5π

3) 30.0π

4) 37.5π

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judziy
Asked by judziyrep:909
University of Benin Nigeria
23 June 2020

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peter
Peter answeredrep:938
University of Lagos Nigeria
12 August 2020
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Volume of a cone, V = 1/3 πr2h

where r is the radius and h is the vertical height.

The vertical height can be found using pythagorean's theorem:

hyp2 = opp2 + adj2

hyp is the slant height

opp is the vertical height

adj is the base

Thus, 6.52 = opp2 + 2.52

subtract 2.52 from both sides

opp2 = 6.52 - 2.52

opp2 = 36

Take square root of both sides,

opp = 6

Therefore, Vertical height = 6

V = 1/3 π(2.5)2(6)

V = 12.5π

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