Question

The radius and the height of the right circular cone are in the ratio 4:3 and its volume is 2156cm3 (3 means cube).Find the csa of the cone.

Answer 1

Solution:-

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
Answer

Answer 2

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