Question

the cost of painting the outer surface of a closed cylindrical oil tank at 60 paisa per sq. cm. is Rs 237.60. The height of the tank is 6 times the radius of the base of the tank. Find height and radius of the tank.

Answer 1

Let the radius = r
height is 6 times the radius,
so height, h= 6r

Rate of painting = 60 paisa per cm²  =Rs. 0.60 per cm²
total cost = Rs 237.60
Total surface area = $\frac{237.60}{0.60} =396\ cm^2$

$TSA=2 \pi r(r+h)\\ \\ \Rightarrow 396=2 \pi r(r+6r)\\ \\ \Rightarrow 396=14 \pi r^2\\ \\ \Rightarrow r^2= \frac{396}{14 \pi } = \frac{396 \times 7}{14 \times 22} =9\\ \\ \Rightarrow r= \sqrt{9}=3cm \\ \\h=6r=6 \times 3=18cm$

Height is 18cm and radius is 3cm.

Answer 2

let the radius = r
then the height = 6r

cost of painting= Rs 237.60
rate of painting = Rs0.60/cm²
outer surface area of cylinder = cost of painting/rate of painting
                                           = 237.60/0.60
                                           =396 cm²
2πrh = 396
2 x π x r x 6r = 396
12 x 22/7 x r² = 396
             396 x 7
r² =      ------------
            12 x 22
r² = 9
r = 3

radius = r = 3
height = 6r = 6 x 3 = 18