Question

A right circular cylindrical container of base radius

6 cm

and height

15 cm

is full of ice cream. The ice cream is to be filled in cones of height

9 cm

and base radius

3 cm

, having a hemispherical cap. Find the number of cones needed to empty the container.

Accepted Answer

Let $h$ and $r$ be the height and radius of the cylinder respectively.

Given that, $h = 15 cm, r = 6 cm$

Volume of the container $V = π r^{2} h$ cubic units.

$= \frac{22}{7} \times 6 \times 6 \times 15$

Let, $r_{1} = 3 cm, h_{1} = 9 cm$ be the radius and height of the cone.

Also, $r_{1} = 3 cm$ is the radius of the hemispherical cap.

Volume of one ice cream cone $=$ (Volume of the cone + Volume of the hemispherical cap)

Volume of one ice cream cone $= ($ Volume of the cone + Volume of the hemispherical cap $)$

$= \frac{1}{3} π r_{1}^{2} h_{1} + \frac{2}{3} π r_{1}^{3}$

$= \frac{1}{3} \times \frac{22}{7} \times 3 \times 3 \times 9 + \frac{2}{3} \times \frac{22}{7} \times 3 \times 3 \times 3$

$= \frac{22}{7} \times 9 (3 + 2) = \frac{22}{7} \times 45$

Number of cones $= \frac{volume of the cylinder}{volume of one ice cream cone}$

Number of ice cream cones needed $= \frac{\frac{22}{7} \times 6 \times 6 \times 15}{\frac{22}{7} \times 45} = 12$

Thus $12$ ice cream cones are required to empty the cylindrical container.

Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 31: Solved Example

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 31: Solved Example

Questions from Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 31: Solved Example with Hints & Solutions

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