Question

Radhika has a vessel, of the form of an inverted cone, open at the top, of height

11 cm

and radius of top as

2.5 cm

and is full of water. Metallic spherical balls each of diameter

0.5 cm

are put in the vessel due to which

{\frac{2}{5}}^{th}

of the water in the vessel flows out. Find out how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

Accepted Answer

Given that height of the conical vessel $= 11 cm,$ radius of top $= 2.5 cm$ .
As conical vessel is full of water, so volume of cone will be equal to the volume of water.
$\Rightarrow$ Volume of water = Volume of cone
$\begin{array}{l} = \frac{1}{3} π r^{2} h \\ = \frac{1}{3} \times π \times (2.5)^{2} \times 11 {cm}^{3} \end{array}$
$\Rightarrow$ Volume of water flows out of cone $= \frac{2}{5}$ of total volume of water
$= \frac{2}{5} \times \frac{1}{3} \times π \times (2.5)^{2} \times 11 {cm}^{3}$
Diameter of metallic spherical ball $= 0.5 cm$
$∴$ Radius of metallic spherical ball $= \frac{1}{2} \times 0.5 cm = 0.25 cm$
Volume of 1 metallic spherical ball $= \frac{4}{3} π r^{3}$
$= \frac{4}{3} \times π \times (0.25)^{3} {cm}^{3}$

Let number of balls put in the vessel be $n$ .
Total volume of $n$ balls $= n \times \frac{4}{3} \times π \times (0.25)^{3} {cm}^{3}$
$∴$ Volume of water flows out $=$ Volume of $n$ balls
$\Rightarrow \frac{2}{5} \times \frac{1}{3} \times π \times (2.5)^{2} \times 11 = n \times \frac{4}{3} \times π \times (0.25)^{3}$
$\Rightarrow n = \frac{2 \times π \times {(2.5)}^{2} \times 11}{5 \times 3} \times \frac{3}{4 \times π \times {(0.25)}^{3}}$
$\Rightarrow n = \frac{2.5 \times 2.5 \times 11}{10 \times (0.25) \times (0.25) \times (0.25)}$
$\Rightarrow n = \frac{2.5 \times 2.5 \times 11 \times 10 \times 10 \times 10}{10 \times (2.5) \times (2.5) \times (2.5)}$
$\Rightarrow n = \frac{1100}{2.5}$
$∴ n = 440$
Values showed are: Conservation of water and natural resources.

Weight(in kg)	Number of students $(f_{i})$
$40 ‐ 44$	$4$
$∴$	$6$
$48 ‐ 52$	$10$
$52 ‐ 56$	$14$
$56 ‐ 60$	$10$
$60 ‐ 64$	$8$
$64 ‐ 68$	$6$
$68 ‐ 72$	$2$

Important Questions on Model Test Paper

Learn and Prepare for any exam you want !