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The radius and height of a circular cone are in the ratio 5 : 12. If its volume is 314 cm3, find its slant height. (Take pi = 3.14)

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11 cm

13 cm

15 cm

18 cm

answer is A.

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Detailed Solution

Given, radius and height of a circular cone are in the ratio 5 : 12 and volume is 314 cm

3

.
Let the radius and height of the cone be 5x and 12x respectively.
For a cone of radius r , slant height l and vertical height h, volume is

13 π r 2 h

.
Then,

13 × 3.14 × (5 x) 2 × 12 x = 314

x 3 = 100 × 112 × 125 × 3

x 3 = 1

x = 1

cm
Then the radius and height are,

r = 5 × x

r = 5 c m

h = 12

cm
We know, slant height

l = r 2 + h 2

l = 52 + 122

l = 169

l = 13

cm
Therefore, the correct option is 1.

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