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Surface Area of Combined Figures

The cross-sec...

Question

The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per $m^{2}$ .

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Solution

Rectangle: Breadth $= 6 \ m, Height = 8 \ m$

Semi-circle: Radius $= 3 \ m$

Length of the tunnel $= 35 \ m$

Surface Area of the tunnel $=$ $\frac{1}{2}$ $2 \pi \times 3 \times 35 + 8 \times 35 \times 2$

$= 330 + 560 = 890 \ m^2$

Cost of plastering $= 890 \times 2.25 = 2002.5 \ Rs.$

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