Question

In the adjoining diagram, a tilted right circular cylindrical vessel with base diameter 7 cm contains a liquid. When placed vertically, the height of the liquid in the vessel is the mean of two heights shown in the diagram. Find the area of wet surface, when the cylinder is placed vertically on a horizontal surface. (Use π = `22/7`).

Answer 1

The cylinder has a base diameter of 7 cm, so the radius r is:

r = `7/2 = 3.5 " cm"`

The heights of the liquid when tilted are h₁ = 1 and h₂ ​= 6 cm.

∴ h = `(h_1 + h_2)/2`

`\implies` h = `1/2(1 + 6)`,

`\implies` h = `7/2`

`\implies` h = 3.5 cm

Area of wet surface = πr² + 2πrh

Area of base = πr² 

= `22/7 xx (3.5)^2`

= 38.5 cm²

Lateral surface area = 2πrh

= `2 xx 22/7 xx 3.5 xx 3.5`

= `2  xx 22/7 xx 12.25`

= 77 cm²

Total wet surface area = Area of base + Lateral area

= 38.5 cm² + 77 cm²

= 115.5 cm²