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In order to provide shelter to flood victims, a shed was constructed using tin sheets which is in the form of cuboid surmounted by a half cylinder as shown below : The length, breadth and height of cuboidal portion are $10$ m, $7$ m and $3$ m respectively. The diameter of the cylindrical portion is $7$ m. Find the cost of tin sheets required to make the shed at the rate of ₹ $70$ per square metre, given that the shed is open from the front side and closed from the back side.
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Area of the sheet required for the shed $= (\text{lateral surface area of the cuboid} - \text{front area}) + \frac{1}{2} CSA \text{ of cylinder} + \text{area of semicircle}$
$= [2 \times (10 + 7) \times 3 - 7 \times 3] + \frac{1}{2} \times 2 \times \frac{22}{7} \times \frac{7}{2} \times 10 + \frac{1}{2} \times \frac{22}{7} \times (\frac{7}{2})^2$
$= \frac{841}{4} m^2$
Cost of sheet $= \frac{841}{4} \times 70 = \text{\text{Rs} } 14717.50$
$= [2 \times (10 + 7) \times 3 - 7 \times 3] + \frac{1}{2} \times 2 \times \frac{22}{7} \times \frac{7}{2} \times 10 + \frac{1}{2} \times \frac{22}{7} \times (\frac{7}{2})^2$
$= \frac{841}{4} m^2$
Cost of sheet $= \frac{841}{4} \times 70 = \text{\text{Rs} } 14717.50$