This is the important question from the cbse board exam point of view because this question was asked in ‘cbse board exam 2012’. Question number 12 from RS Aggarwal book page number 787, exercise 17A. Chapter Volume and surface area of solid.
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A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.
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From given information
The radius of hemisphere and the radius of cone (r) = 3.5 cm,
Total height of the solid is 9.5 cm.
height of hemisphere is equal to the radius of hemisphere.
Height of the cone = Total height of solid – height of hemisphere
Height of the cone (h) = 9.5 – 3.5 = 6 cm
Volume of the solid = Volume of the hemisphere + Volume of the cone
Volume of the solid =
Substitute respective values.
Volume of the solid =%5E3%2B%5Cfrac%7B1%7D%7B3%7D%5Ctimes%5Cfrac%7B22%7D%7B7%7D%5Ctimes(3.5)%5E2(6))
Volume of the solid =
Volume of the solid = 89.83+77
Volume of the solid = 166.83
∴ Volume of the solid is 166.83 cm³