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Q.

A cylindrical pillar is 50cm in diameter and 3.5m in height. Find the cost of painting the curved surface area of the pillar at the rate of 12.50 per $m 2$ .

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a

Rs.68.75.

b

Rs.58.75.

c

Rs.48.75.

d

Rs.88.75.

answer is A.

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Detailed Solution

Here, the diameter of the base of the cylindrical pillar is 50 cm and the height of the cylindrical pillar is 3.5 m. We need to find out the cost of painting the curved surface of the cylindrical pillar. For this purpose, we first find the value of the curved surface of the cylindrical pillar. The curved surface of the cylinder is given by

where r is the radius and h is the height of the cylinder.
Now the diameter is given as 50 cm, so the radius will be half the diameter. Therefore, the radius,

⇒ 502 = 25 c m ⇒ r = 25 c m

H = 3.5m (Given)
1 meter = 100 centimeters.

1 centimeter = 1100 meter ⇒ 25 c m = 25100 m = 14 m = 0.25 m

Now, r = 0.25m and h = 3.5m.
Therefore,

C S A = 2 π r h ⇒ (2 × 227 × 0.25 × 3.5) m 2 ⇒ (44 × 0.125) m 2 ⇒ 5.5 m 2

Hence, the curved surface area of the cylindrical pillar is

5.5 m 2

.
Now, the cost of painting

1 m 2

is given as Rs.12.50.
Therefore, the cost of painting

5.5 m 2

will be equal to,

⇒ 12.50 × 5.5 = R s .68.75

Hence, the cost of painting the curved surface area of the cylindrical pillar is Rs.68.75.

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