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Horse stable is in the form of a cuboid, whose external dimensions are 70 m $×$ 35 m $×$ 40 m surrounded by a cylinder halved vertically through diameter 35m and it is open from one rectangular face 70 m $×$ 40 m. The cost of painting the exterior of the stable at the rate of Rs. 2 per m2 is

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Rs. 25000

Rs. 22000

Rs. 20000

Rs. 18900

answer is D.

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Detailed Solution

Given, L=70m,
B=35m and
H = 40m. Lateral surface area of a cuboid is the area of four walls i.e. 2(l+b)h.

Area of four walls = 2 (70 + 35) × 40 ⇒ 8400 m 2

We need curved surface area of half cylinder so,
Putting R= (

352

) and H=70.
We know that, CSA of Cylinder = 2πrh.

Area of top cylinder= 12 × 2 × 227 × 352 × 70 ⇒ 3850 m 2

Area of open side is

⇒ 40 × 70 ⇒ 2800 m 2

Area to be painted = Area of four walls + area of top cylinder – area of open area side

⇒ 8400 + 3850 - 2800 ⇒ 9450 m 2

The cost of painting the exterior of stable is

⇒

9450 × 2 = Rs .1 8900

Therefore, the correct option is 4.

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