Mensuration-42

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A cylindrical cistern whose diameter is 14 cm is partially filled with water. If a conical block of iron
whose radius of the base is 3.5 cm and height 6 cm is wholly immersed in the water, by how much will the water level rise ?

Solution: For cone, r = 3.5 cm = 7/2 cm, h = 6 cm

Volume of cone = 1/3 x Π r2 h = 1/3 x 22/7 x 7/2 x 7/2 x 6 = 77 cm3 -------- (1)

Radius of the cistern = 14/2 cm = 7 cm. Let the water level rise to h cm. Then

Volume of water in the cistern = Π r2 h = (22/7 x 7 x 7x h) cm3 ----------- (2)

From (1) and (2), we have

22/7 x 7 x 7 x h = 77

=> h = (77 x 7) / (22 x 7 x 7) = 1/2 = 0.5

Hence, the water level will rise to a height of 0.5 cm

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