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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 metallic disc, in the shape of a right circular cylinder, is of height 2.5 mm and base radius 12 cm. Metallic disc is melted and made into a sphere. Calculate the radius of the sphere.
Solution:
When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is.
Given height of the cylinder, h = 2.5 mm = 0.25 cm
Radius of the cylinder, r = 12 cm
Volume of the cylinder = π r2h
= π 122×0.25
= π 144×0.25
= 36 π cm3
Let R be the radius of the sphere.
Volume of sphere = (4/3)π R3
Since metallic disc is melted and made into a sphere, their volumes remains same.
(4/3)π R3 = 36π
R3 = 36×3/4
R3 = 27
Taking cube root
R = 3 cm
Hence the radius of the sphere is 3 cm.
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