Finding Height of a cone when ratio of Radius and Height with volume is given.

Question of The Day16-05-2022

The radius and height of a right circular cone are in the ratio 3 : 7. If the volume of the cone is 528 cm³. Then what is the height of the cone? (Take π = 22/7)

Answer

Correct Answer : d ) 14 cm

Explanation :

Let the radius of cone be 'r'.

Let the height of the cone be 'h'.

It is given that

The ratio of radius and height of the cone is r : h = 3 : 7

r/h = 3/7

r = 3h/7 ......(1)

Volume of the cone (V) = 528 cm³

We know that,

Volume of the cone (V) = (1/3)πr²h

(1/3)πr²h = 528 .....(2)

Putting eq. 1 in eq. 2

(1/3)π(3h/7)²h = 528

(22 * 9 * h³)/(3 * 7 * 49) = 528

h³ = 528 * 3 * 7 * 49/ (22 * 9)

h³ = 2744

h = 14

Hence, (d) is the correct answer.

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