Question

Please help me solve this!!

The cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq dm is 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume.

Please solve this, and mention how did you arrive to the conclusion. (20 points) :)

Answer 1

Let the Radius of the cylinder be x meter
r = x
h = 6 times r = 6x

Cost = area×rate
237.60 = area×60
Area = 3.96 dm

T.S.A of the Cylinder = 2πrh+2πr^2 = 2πr(r+h)

3.96 = 2×(22/7) × x × (x+6x)
3.96 = (44/7) × x × 7x
3.96 = 44x^2
x^2 = 0.09

Volume of Cylinder = πr^2h
= π × (x^2) × (6x)
= (22/7) × 0.09 × (6×0.3)
= 22/7 × 0.09 × 1.8
= 0.509 cubic dm

Answer 2

Given,
Let r be its radius and h be its height.
Height = h = 6 times its radius = 6r
Then,
T.S.A = 2πr(r+h)
         = 2πr(r+6r)
         = 2 × 22/7 ×7r
         = 44r²
Now,
Cost of painting = 60 p/dm²
In Rs. = 0.6/dm²
Cost of painting 1 dm² = Rs.0.6
Then, Cost of 44r² dm² = Rs.0.6×44r²
Total cost = Rs.237.60
∴0.6 × 44r² = 237.60
⇒r² = 237.60/44 × 0.6
⇒r² = 9
⇒r = √9
⇒r=3
 So, Radius of the cylindrical oil tank is 3 dm
∴ Height =  h = 6 × 3 = 18 dm
 
Now, we need to find volume:
We know it is cylindrical oil tank.
So, 
Volume = πr²h
             = 22/7 × ( 3 dm)² × 18
             = 509.14 dm²