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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration
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The volume of a cone is the same as that of the cylinder whose height is 9 cm and diameter 40 cm. Find the radius of the base of the cone if its height is 108 cm.
Solution:
Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. Sometimes, volume is also termed as capacity.
Given height of the cylinder, h = 9 cm
Diameter of the cylinder = 40 cm
Radius of the cylinder, r = 40/2= 20 cm
Volume of the cylinder =π r2h
= π 202×9
= π ×400×9
= 3600π cm3
Height of the cone, H = 108 cm
Volume of cone = (1/3)π r2h
= (1/3)π r2×108
= 36π r2
Since volume of cone is equal to the volume of the cylinder, we get
36π r2 = 3600π
r2 = 3600/36
r2 = 100
Taking square root on both sides,
r = 10 cm
Hence the radius of the cone is 10 cm.
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