Question

If there is a cone whose radius and height are in the ratio of 6:3 . Find the volume and triangular area 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

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