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Question

The radius and height of a cone are in the ratio 1:2. If its volume is 144π cm3, its slant height = .

A
55 cm
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B
65 cm
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C
45 cm
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Solution

The correct option is B 65 cm
Volume of a cone = 13 πr2h
Given that rh=12
r= h2.
Therefore, volume
= 13π(h2)2×h
= 112πh3
Volume is given to be 144π cm3.
112πh3 = 144 π
h3 = 144 × 12
h=12 cm
r=6 cm
Now, slant height
=h2+r2
= 122+62
=180
= 6 5 cm
Therefore, slant height is 65 cm long.

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