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Find (ii) how much steel was actually used, if 1/12 of the steel actually used was wasted in making the tank.

Q : 9    Find (ii)  how much steel was actually used, if $\small \frac{1}{12}$  of the steel actually used was wasted in making the tank.

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Given, a closed cylindrical petrol tank.

The diameter of the tank = $\small d = 4.2\hspace{1mm}m$

Height of the tank = $\small h = 4.5\hspace{1mm}m$

Now, Total surface area of the tank = $2\pi r (r + h)$

$\\ = 2 \times \frac{22}{7} \times 2.1 \times (2.1 + 4.5) \\ = (44 \times 0.3 \times 6.6) \\ = 87.12\ m^2$

Now, let $x\ m^2$ of steel sheet be actually used in making the tank

Since $\small \frac{1}{12}$ of steel was wasted, the left $\small \frac{11}{12}$ of the total steel sheet was used to made the tank.
$\small \therefore$ The total surface area of the tank = $\small \frac{11}{12}\times (Total\ area\ of\ steel\ sheet )$
$\small \\ \Rightarrow 87.12= \frac{11}{12}x \\ \Rightarrow x = \frac{87.12\times12}{11} \\ \Rightarrow x = 95.04\ m^2$

Therefore, $\small 95.04\ m^2$ of steel was actually used in making the tank.

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