Question

The radius and height of a solid right circular cone are in the ratio of 5:12. If its volume is 314 cm2
,find its total surface area.( = 3.14)

Answer 1

Answer:

Ratio of radius and height of a right circular cone is 5:12

let the radius and height be 5x and 12x respectively

The slant height of cone by Pythagoras theorem will be 13x (5x^2+12x^2= slant height ^2 means l^2)

volume of cone is 314 cm cube

hence 1/3πR^2H=314 (π=3.14 -given)

1/3×3.14×5x^2×12x=314

1/3×25x^2×12x=314÷3.14

25x^2×4x=100

100x^3=100

x^3=1

x=1

so Radius of cone=5x=5cm

Height of cone=12x=12cm

and slant height of cone (l)=13x=13cm

Now, TSA of cone= πRl+πR^2

=πR(l+R)

=3.14×5(13+5)

=15.7×18

=282.6cm square