Question

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.

• A. 10
• B. 30
• C. 25
• D. 20

Answer 1

The correct option is A

10

Let number of cones which can be filled = n

Diameter of cylinder = d = 12 cm

$\Rightarrow$ Radius of cylinder =
$r=\frac{d}{2}=\frac{12}{2}=6cm$

Height of cylinder = h = 15 cm

Volume of cylinder = $\pi .r^2.h=(\pi \times 6^2\times 15)=540\pi c{m}^3$

Diameter of cone = $d_1=6cm$

Radius of cone = $r_1=\frac{d_1}{2}=\frac{6}{2}=3cm$

Height of cone = $h_1=12cm$

Volume of cone $=\frac{1}{3}\pi (r_1{)}^2{h}_1=\frac{1}{3}\times \pi \times 3^2\times 12=36\pi {\text{cm}}^3$

Radius of hemispherical top of the cone = $r_1=3cm$

Volume of hemisphere top $=\frac{2}{3}\pi (r_1{)}^3=\frac{2}{3}\times \pi \times 3^3=18\pi {\text{cm}}^3$

According to given condition we have:

n × ( Volume of Cone + Volume of Hemispherical top ) = volume of cylinder

$\Rightarrow$ n × (36 $\pi +18\pi )=540\pi$

$\Rightarrow$ n × (54 $\pi )=540\pi$

$n=\frac{540}{54}=10$