Question

The radius and height of the cone are in the ratio 5:12 and volume is 314m. Find slant height

Answer 1

1/3*3.14*25*12*x^3=314
x=1
then
l=13

Answer 2

Ratio of radius and height of cone = 5:12
So, Let radius = 5x and height=  12x
Volume of cone = 314m
(1/3)πr²h           =  314
1 × 3.14 × 5x × 5x  × 12x  / 3  = 314
                           x³  = (314 × 3)/25 ×12×3.14
                           x³   = 1
                         ⇒ x = 1
So, Radius = 5x = 5×1= 5m
       Height = 12x= 12×1 = 12
We know that $slant height(l)= \sqrt{ h^{2} + r^{2} }$
                       $So, l(slant height) = \sqrt{ 12^{2} + 5^{2} }$
                                                           = √169 = 13m
So, slant height of cone = 13m