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If the diameter of the base of a right circular cone is 28 cm and its volume is $9856 c m 3 .$

What would be the height of the cone?

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45 cm

46 cm

47 cm

48 cm

answer is D.

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Detailed Solution

It is given that the cone’s volume is

9856 c m 3

and its diameter is 28 cm.

∴ r = 282 =14 cm  and V = 9856 cm 3 .

We know that the volume of the cone is

13 π r 2 h,

where r is the radius of the base and h is the cone's height.
Let’s assume that the height of the cone be

h c m .

∴ V = 13 π r 2 h ⇒ 9856 = 13 × 227 × 14 × 14 × h ⇒ 9856 = 13 × 616 × h ⇒ h = 9856 × 3 × 1616

⇒ h = 9856 × 3 × 1616 ⇒ h = 48 cm

Therefore the height of the cone will be 48 cm.
Hence, option (4) is correct.

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