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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 0 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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23 June 2020 University of Lagos Nigeria
12 August 2020 0 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:

hyp is the slant height

opp is the vertical height

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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