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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration
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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.
Solution:
Here we can find the required total surface area of the can by adding the curved surface area and base area of the cylinder.
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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