A right circular cylinder having a diameter 12cm and height 15cm is full of ice-cream. The ice-cream is to be filled in cones of height 12cm and diameter 6cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

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answer is D.

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Detailed Solution

Concept- Here, we must first use the formula

to determine the cylinder's volume. The volume of the ice cream cone with a hemispherical shape must then be determined. To do this, we must first determine the volume of the cone using the formula

and then determine the volume of the hemisphere using the formula

. In this case, the hemisphere's radius and the cone's radius will be equal. Finally, determine the number of cones, which is equal to the cylinder's volume divided by the total of the cone and hemisphere volumes.
A right circular cylinder filled with ice cream is presented to us. The cylinder's height and diameter are,
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Therefore, the cylinder's radius

The cylinder's volume,

, must next be determined. It is provided by
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Consequently, the cylinder's volume is determined by

The ice cream must then be placed within a cone with a hemispherical top.
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The cone's height and diameter are given as,
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Consequently, the cone's radius

The cone's volume must next be determined. Cone

’s volume is determined by,
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Therefore,

is the formula for the cone's volume.
The diameter of the cone and the hemisphere are identical since the cone has a hemispherical top.
Consequently, the hemisphere's diameter is determined by
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In other words,

is the hemisphere's radius.
The hemisphere's volume must then be determined. The formula for calculating hemispheric volume

As a result,

gives the hemisphere's volume.
The quantity of cones that can hold ice cream must now be determined.
Finding the number of ice cream cones, n, involves:
Question Image

Hence, the correct answer is option 4.

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