Question

The cost of painting total outside surface of a closed cylindrical box at Rs 10 cm' is Rs 1540
The height of the tank is equal to its radius. Find the volume of cylindrical tank.​

Answer 1

Answer:

The volume of cylindrical tank is 134.75 cm³.

Step-by-step explanation:

Given: Total cost of painting = Rs 1540 , Rate of painting = Rs 10 per cm and height is equal to the radius of the tank.

If radius of the tank is r cm and its height is h cm, then h = r.

w.k.t., total outside surface area of cylinder is 2πr(r+h) and volume of cylinder is πr²h.

⇒ Total surface area of cylinder = 2πr(r+h) = 2πr(r+r) = 4πr²

⇒ Total cost of painting = (total surface area of cylinder) × (rate of painting)

⇒ 1540 = 4πr² × 10

⇒ r² = 1540 / 40π

⇒ r² = (77 × 7) / (2 × 22)

⇒ r² = 49/4

⇒ r = 7/2 = 3.5 cm

⇒ h = r = 3.5 cm

So, volume of cylinder = πr²h = (22 × 3.5 × 3.5 × 3.5) / 7

⇒ Volume of cylinder = 134.75 cm³

Answer 2

Let r dm be the radius of the base and h dm be the height of the cylindrical tank.

Then, h=6r (given)

Total surfacea area =2πr(r+h)=2πr(r+6r)=14πr2

cost of painting =Rs.(14πr2)×10060​=Rs542​r2

It is given that the cost of painting is Rs. 237.60

∴542​πr2=237.60⇒542​×722​×r2=237.60

⇒r2=237.60×425​×227​=9⇒r=3dm

∴h=6r=18dm

Hence, volume of the cylinder =πr2h=(π×3×3×18)dm3=(722​×9×18)dm3=