M.L Aggarwal book Important Question of class 10 chapter Based on Mensuration for ICSE BOARD.
If the ratio of the radii of two sphere is given.
Find the ratio of their volumes and the ratio of their surface areas.
This is the Question Number 10, Exercise 17.3 of M.L Aggarwal.
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(a) If the ratio of the radii of two sphere is 3 : 7, find : (i) the ratio of their volumes. (ii) the ratio of their surface areas. (b) If the ratio of the volumes of the two sphere is 125 : 64, find the ratio of their surface areas.
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(i)Let the radii of two spheres be r1 and r2.
Given ratio of their radii = 3:7
Volume of sphere = (4/3)r3
Ratio of the volumes = (4/3)r13/(4/3)r23
= r13/ r23
= 33/73
= 27/343
Hence the ratio of their volumes is 27:343.
(ii)Surface area of a sphere = 4r2
Ratio of surface areas of the spheres = 4r12/4r22
= r12/r22
= 32/72
= 9/49
Hence the ratio of the surface areas is 9:49.
(b)Given ratio of volume of two spheres = 125/64
(4/3)r13/(4/3)r23 = 125/64
r13/ r23 = 125/64
Taking cube root on both sides
r1/r2 = 5/4
Ratio of surface areas of the spheres = 4r12/4r22
= r12/r22
= 52/42
= 25/16
Hence the ratio of the surface areas is 25:16.