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The cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per $sq . m$ is $₹ 237.60$ the height of the tank is 6 times the radius of the base of the tank. Find the height of the tank. $[take π = \frac{22}{7}]$

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15 m

16 m

17 m

18 m

answer is D.

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Detailed Solution

Given that, height of tank is 6 times the radius of the base of tank.
The cost is

₹

237.60 at rate of 60 paise per sq. m.
Converting 60 paise to

₹ 1

using

₹ 1 = 100 paise .

So, 60 paise =

₹ 0.6

Now divide the total cost by rate to find total surface area.

\Rightarrow \frac{237.60}{0.6} = 396 sq . m

Total surface area of cylindrical oil tank is,
TSA=

2 πr (h + r)

, here r is radius, h is height.
As per the question,

h = 6 r

.
So,
TSA =

2 πr (6 r + r)

\Rightarrow 396 = 2 \times \frac{22}{7} \times r (7 r)

\Rightarrow 396 = 2 \times 22 \times r^{2}

\Rightarrow r^{2} = 9

\Rightarrow r = 3

Now substitute the value

r = 3 m

in the equation of h,

\Rightarrow h = 6 (3)

\Rightarrow h = 18 m

So, the height of the tank is 18m.
Therefore, option (4) is correct.

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