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

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answer is A.

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Detailed Solution

Given,
Diameter of right circular cylinder = 12 cm
Height of right circular cylinder = 15 cm
Cone height = 12 cm
Cone diameter = 6 cm
Radius of the cone = 3 cm
Number of ice-cream cones = N
C:UserssoftberryDownloadsP0041 JPEGQ.12.jpg

C:UserssoftberryDownloadsP0041 JPEGQ.12.jpg

Calculation
1st we have find the volume of circular cylinder

= π r^{2} h

= π \times 6 \times 6 \times 15 {cm}^{3}

2nd again find the volume of one ice-cream cone

= \frac{1}{3} π r^{2} h

= \frac{1}{3} \times π \times 3 \times 3 \times 12 {cm}^{3}

3rd find the volume of hemisphere of the cone

= \frac{2}{3} π r^{3}

= \frac{2}{3} \times π \times 3 \times 3 \times 3 {cm}^{3}

We have obtain the all required value. Put in the formula which is

Number of ice cream cones = \frac{volume of cylinder}{volume of cone + hemisphere}

N = \frac{π \times 6 \times 6 \times 15 {cm}^{3}}{\frac{1}{3} \times π \times 3 \times 3 \times 12 {cm}^{3} + \frac{2}{3} \times π \times 3 \times 3 \times 3 {cm}^{3}}

N = \frac{π \times 36 \times 15}{\frac{π}{3} \times (108 + 54)}

N = 10

Hence the number of cones = 10.
Correct option is 1.

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