A petrol tank is a cylinder of base diameter $ 21 \mathrm{~cm} $ and length $ 18 \mathrm{~cm} $ fitted with conical ends each of axis length $ 9 \mathrm{~cm} $. Determine the capacity of the tank.

Academic Mathematics NCERT Class 10

Given:

A petrol tank is a cylinder of base diameter \( 21 \mathrm{~cm} \) and length \( 18 \mathrm{~cm} \) fitted with conical ends each of axis length \( 9 \mathrm{~cm} \).

To do:

We have to find the capacity of the tank.

Solution:

Diameter of the cylindrical part $= 21\ cm$

This implies,

Radius of the cylindrical part $r = \frac{21}{2}\ cm$

Height of the cylindrical part $h_1 = 18\ cm$

Height of each conical part $h_2 = 9\ cm$

Total volume(capacity) of the tank $=2 \times \frac{1}{3} \pi r^{2} h_{2}+\pi r^{2} h_{1}$

$=\pi r^{2}(\frac{2}{3} h_{2}+h_{1})$

$=\frac{22}{7}\times(\frac{21}{2})^{2}(\frac{2}{3} \times 9+18)$

$=\frac{22}{7} \times \frac{441}{4}(6+18)$

$=\frac{11 \times 63}{2} \times 24$

$=8316 \mathrm{~cm}^{3}$

The capacity of the tank is $8316\ cm^3$.

Simply Easy Learning

Updated on: 10-Oct-2022

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