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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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N Nehul

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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