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A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, 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 C.

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Detailed Solution

Given:
Cylindrical container height

(h_{1})

= 15 cm

Circular end of container radius

(r_{1})

= \frac{12}{2} = 6 cm

circular end of ice-cream cone radius

(r_{2})

= \frac{6}{2} = 3 cm

Conical part of ice-cream cone height

(h_{2})

= 12 cm

Suppose that
Ice-cream cones be filled with ice-cream of the container = n
Now calculate the volume of ice-cream in cylinder,
= n (1 ice-cream cone volume + hemispherical shape on the top volume)

π r_{1}^{2} h_{1} = n (\frac{1}{3} π r_{2}^{2} h_{2} + \frac{2}{3} π r_{2}^{3})

\Rightarrow π \times 6^{2} \times 15 = n (\frac{1}{3} π 3^{2} \times 12 + \frac{2}{3} π 3^{3})

\Rightarrow n = \frac{30 \times 15}{\frac{1}{3} \times 9 \times 12 + \frac{2}{3} \times 27}

\Rightarrow n = \frac{36 \times 15 \times 3}{108 + 54}

n = 10

Hence, ice-cream cones can be filled with the ice-cream in the container = 10
Option 3 is correct.

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