Q) 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 = 22/7)

ICSE Specimen Question Paper (SQP)2025

Ans: Step 1: Given: base diameter = 7 cm

∴ base radius, r = cm

When placed vertically, height h = = 3.5 cm

Step 2: Area of wet surface = Area around the vessel’s walls + Base area

= 2 π r h + π r

= π r (2 h + r)

Step 3: By substituting the values of r and h, we get:

Area of wet surface = π r (2 h + r)

= (3.5) [ 2 (3.5) + 3.5 ]

= (3.5) (10.5)

= 22 x 0.5 x 10.5 = 11 x 10.5

= 115.5 cm²

Therefore, total wet surface Area of the vessel is 115.5 mm² 

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