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

Question 31 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 total surface area of the can in contact with water when the sphere is in it.



Here we can find the required total surface area of the can by adding the curved surface area and base area of the cylinder.

M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Mensuration Question 31 Solution image

Given radius of the cylinder, r = 3.5 cm

Diameter of the sphere = height of the cylinder

= 3.5×2

= 7 cm

So radius of sphere, r = 7/2 = 3.5 cm

Height of cylinder, h = 7 cm

Total surface area of can in contact with water = curved surface area of cylinder+base area of cylinder.

= 2π rh+π r2

= π r(2h+r)

= 22/7)×3.5×(2×7+3.5)

= (22/7)×3.5×(14+3.5)

= 11×17.5

= 192.5 cm2

Hence the surface area of can in contact with water is 192.5 cm2.

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