Question

A water tank of cylindrical shape has diameter 1 m and height 2 m. Tank is closed with lid. The tank is to be painted internally and externally including the lid.
Find the expenditure if the rate of painting is ₹ 80 per sqm. ( π = 3.14)

Answer 1

According to the question,

diameter = 1m or, radius(r) = diameter/2 = 1/2 = 0.5m

height(h) = 2m.

Now, we know that surface area of a cylinder is given by 2πr(h+r)

or, 2 x π x 0.5(2 + 0.5) = 2 x 3.14 x 0.5 x 2.5 = 7.85 square metre.

Since the tank is to be painted both from inside and outside, so it is quite sure that the surface area will be simply twice i.e. Total surface area = 2 x 7.85 = 15.7 square metre.

Now, if the rate of painting is ₹ 80 per sqm then, for painting 15.7 sqm the cost incurred = Rs 80 x 15.7 = Rs 1256.(Ans)

Answer 2

radius of cylindrical tank , r = 1/2 = 0.5 m
height of cylindrical tank , h = 2m
so, surface area of tank = 2πrh
= 2 × 3.14 × 0.5 × 2
= 6.28 m²
a/c to question,
tank is closed with lid.
so, surface area of lid = 2πr²
= 2 × 3.14 × 0.5 × 0.5
= 3.14 × 0.5 = 1.57 m²
hence, total surface area = 1.57 + 6.28 = 7.85 m²

because the tank is to be painted internally and externally including the lid , total area to be painted = 2 × area of tank
= 2 × 7.85 = 15.7 m²

now, expenditure = total area × rate of painting
= 15.7 × 80 = 1256

hence, answer is ₹ 1256