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Q.

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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a

11 cm 

b

13 cm

c

15 cm

d

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 1 3 π r 2 h  .
Then,
  1 3 ×3.14× (5x) 2 ×12x=314   x 3 =100× 1 12 × 1 25 ×3   x 3 =1   x=1   cm
Then the radius and height are,
r=5×x  
r=5cm   h=12   cm
We know, slant height l= r 2 + h 2   l= 5 2 + 12 2   l= 169   l=13   cm
Therefore, the correct option is 1.
 
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