A tank is in the shape of a cylinder with two hemispheres attached to both ends as shown in the figure. Its common diameter is $2 m$ and total length is $8 m$ .
Find the total cost of painting the outer surface of this tank at the rate of $Rs. 60$ per square metre. (use $π = 3.14$ as an approximation)

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Solution

Given, Common diameter $= 2 m$
Radius $= 1 m$
Total length of tank $= 8 m$
Length of cylinder $= h = 8 - 2 (1) = 6 m$

Surface area of the tank
= Surface area of two hemispheres + lateral surface area of the cylinder
$= 2 \times 2 π r^{2} + 2 π r h$
$= 2 π r (2 r + h)$
$= 2 \times 3.14 \times 1 (2 \times 1 + 6)$
$= 50.26 m^{2}$

Cost of painting $= 50.26 \times 60 = Rs. 3015.92$
$∴$ Cost of painting the tank is $Rs.$ $3015.92$

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A tank is in the shape of a cylinder with two hemispheres attached to both ends as shown in the figure. Its common diameter is 2 m and total length is 8 m. Find the total cost of painting the outer surface of this tank at the rate of Rs. 60 per square metre. (use π=3.14 as an approximation)