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An ice cream cone full of ice cream having a radius of 5 cm and a height of 10 cm is shown in figure below. What is the volume of ice cream, provided that it’s $16$ the part is left unfilled with ice cream?

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327.4 cm³

350 cm³

369.2 cm³

370.0 cm³

answer is A.

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Detailed Solution

Given that the radius of the ice-cream cone is 5cm and height is 10cm.
And the volume of the hemisphere of radius 5cm:
Volume of the hemisphere of radius 5cm,

V = 23 π r 3 V = 23 × 227 × 53 V = 550021 V = 261.90 c m 3

Now, height of cone H is:

H = 10 − 5 H = 5 c m

So, volume of a cone,

V' = 13 π R 2 H V' = 13 × 227 × 52 × 5 V' = 275021 V' = 130.95 c m 3

Now, the total volume of the ice-cream:

V + V' = 261.90 + 130.95 V + V' = 392.85 c m 3

As given the

16 t h

part is left unfilled with ice-cream, the volume of an ice-cream will be,

⇒ 392.85 − 16 392.85 ⇒ 392.85 − 65.475 ⇒ 327.4 c m 3

Therefore, 1 is the correct answer.

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