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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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n = 10

n = 12

n = 14

n = 18

answer is A.

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Detailed Solution

Given,
Height

(h_{1})

of cylindrical container is 15 cm and diameter is 12 cm,
So,

Radius = \frac{Diameter}{2}

Circular end or container radius

(r_{1})

= \frac{12}{2}

Radius

(r_{1})

= 6 cm

Radius

(r_{2})

of circular end of ice-cream cone,

(r_{2}) = \frac{6}{2}

(r_{2}) = 3 cm

Ice-cream conical part Height

(h_{2})

= 12 cm

Suppose that “

x

” ice-cream cones can be filled with the ice-cream in the container. Now, the volume of ice-cream in cylinder,
V=

x

(Volume of ice-cream cone + Volume of hemispherical shape)

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

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

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

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

x = \frac{1620}{162}

x = 10

Hence, “

10

” ice-cream cones can be filled with the ice-cream in the container.
The Correct Answer is 1.

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