Question

A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take $\pi =\frac{22}{7}$)

Answer 1

Given:
Radius of cylindrical container, $r_c$ = 10 cm
Height of cylindrical container, $h_c$ = 35.2 cm
Radius of cylindrical glass, $r_g$ = 4 cm
Height of cylindrical glass, $h_g$ = 10 cm

Volume of the cylindrical container $=\pi {r_c}^2{h}_c=\pi \times {10}^2\times 35.2$

Volume of the glass $=\pi {r_g}^2{h}_g=\pi \times 4^2\times 10$

Number of glasses of juice that are sold $=\frac{\text{volume of the cylindrical container}}{\text{volume of each glass}}$

$=\frac{\pi \times 10\times 10\times 35.2}{\pi \times 4\times 4\times 10}$

$=22$

$\therefore$ The amount received by the juice seller = cost of each glass $\times$ number of glasses sold
$=\text{₹}10\times 22=\text{₹}220$

[Alternatively,
Volume of the cylindrical container $=\pi {r_c}^2{h}_c=\pi \times {10}^2\times 35.2$
Volume of the glass $=\pi {r_g}^2{h}_g=\pi \times 4^2\times 10$
Given that the seller charges ₹ 10 for a glass of height 10 cm and and radius 4 cm.
i.e., the seller charges ₹ 10 for a volume of ${}^{\prime }\pi \times 4^2\times {10}^{\prime }$
Hence, the amount to be charged for a volume of ${}^{\prime }\pi \times {10}^2\times {35.2}^{\prime }$ is,
$\frac{(\pi \times {10}^2\times 35.2)\times 10}{\pi \times 4^2\times 10}$
$=₹220$]