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.

Given

Radius of cylinder (r) = 6 cm

Height of cylinder (h) = 15 cm

Radius of each cone (R) = 3 cm

Height of each cone (H) = 12 cm

Find out

We have to find the number of cones

Solution

Let the total number of ice creams cones be = n

Number of cones = Volume of cylinder / Volume of ice cream cone

The volume can be expressed as

n × (Volume of each Cone + Volume of each hemisphere) = Volume of Cylinder

n × (1/3πR2H + 2/3πR3) = πr2h

On cancelling π from both sides we get

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

n = $$\frac{36\times 15}{\frac{1\times9\times12\times2\times27}{3}}$$

n = $$\frac{36\times 15}{\frac{162}{3}}$$

n = $$\frac{540}{54}$$

n = 10

Hence, 10 numbers of cones filled with ice-cream.