ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 30 Mensuration Exercise 17.5

A cylindrical can whose base is horizontal and of radius 3.5 cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate : the depth of the water in the can before the sphere was put into the can. Given your answer as proper fractions.



Here to find the volume of the cylindrical can, we need to add the volume of sphere to the volume of water present in the cylindrical can.

M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Mensuration Question 30 Solution image

Let the depth of the water before the sphere was put be d.

Volume of cylindrical can = volume of sphere+ volume of water

π r2h = (4/3)π r3+π r2d

π r2h = π r2{(4/3)r +d)}

h = (4/3)r +d

d = h – (4/3)r

d = 7 – (4/3)×3.5

d = (21-14)/3

d = 7/3

Hence the depth of the water before the sphere was put into the can is 7/3 cm.

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