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Probability

Question
CBSEENMA9003412

The cost of painting the total outside surface of a closed cylindrical tank at 60 paise per sq. d.m. is र 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places.

Solution
Curved surface area  equals fraction numerator 237.60 over denominator 0.60 end fraction

= 396 dm2
Let the radius of the base of the tank be r dm. Then, height = 6 r dm
∴ Curved surface area = 2πRH
equals 2. straight pi. straight r. left parenthesis 6 straight r right parenthesis
equals 2.22 over 7. straight r left parenthesis 6 straight r right parenthesis
equals 264 over 7 straight r squared space dm squared
According to the question,
264 over 7 r squared equals 396
rightwards double arrow space space r squared equals fraction numerator 396 cross times 7 over denominator 264 end fraction equals 21 over 2
rightwards double arrow space r equals square root of 21 over 2 end root space d m
therefore space space space space v equals πr squared straight h equals 22 over 7.21 over 2. open parentheses 6 square root of 21 over 2 end root close parentheses
= 198 x 3.24 = 641.52 dm3