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

Last updated date: 22nd Mar 2023

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Answer

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Hint: To find the number of cones, first we will find the volume of the circular cylinder and divide it with the volume of one ice-cream cone.

So,

Number of cones volume of the circular cylinder ÷ volume of one ice-cream cone

= $\dfrac{{\pi \times 6 \times 6 \times 15}}{{\dfrac{1}{3} \times \pi \times 3 \times 3 \times 12 + \dfrac{{2\pi }}{3} \times {3^2}}} = \dfrac{{\pi \times 36 \times 15}}{{\dfrac{\pi }{3} \times \left( {108 + 54} \right)}} = 10$

Answer $10$ cones

Note: In these questions, make sure you take the volume of the entities and not the area or perimeter.

Remembering the volume formulas is often helpful.

So,

Number of cones volume of the circular cylinder ÷ volume of one ice-cream cone

= $\dfrac{{\pi \times 6 \times 6 \times 15}}{{\dfrac{1}{3} \times \pi \times 3 \times 3 \times 12 + \dfrac{{2\pi }}{3} \times {3^2}}} = \dfrac{{\pi \times 36 \times 15}}{{\dfrac{\pi }{3} \times \left( {108 + 54} \right)}} = 10$

Answer $10$ cones

Note: In these questions, make sure you take the volume of the entities and not the area or perimeter.

Remembering the volume formulas is often helpful.

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