Question

the radius and height of aright circular cone are in the ratio 4:3 and its volume is 2156cu.cm find the curved surface area and the total surface area of the cone​

Answer 1

Let the radius and height of the right circular cone be 'r' and 'h' respectively.

Now, it is given that

r/h = 4/3

h = 3r/4

Volume of the cone = 2156 cu cm (given)

Volume of the cone = 1/3πr²h

⇒ 2156 = 1/3*22/7*r²*3r/4

⇒ 66r³ = 2156*84

⇒ r³ = 181104/66

⇒ r³ = 2744

⇒ r = ∛2744

⇒ r = 14 cm

So, h = (3*14)/4

h = 21/2 cm = 10.5 cm 

Now, let the slant height of the cone be 'l'.

we know that,

l² = r² + h²

l² = 14² + 110.5²

l² = 196 + 110.25

l² = 306.25

l = √306.25

l = 17.5 cm

Now, Curved surface area of the cone = πrl

= 22/7*14*17.5

= 5390/7

CSA of the cone = 770 sq cm