Q18 of 79 Page 229

Radii of two solid hemispheres are in the ratio 3 : 5. Find the ratio of their curved surface areas and the ratio of their total surface areas.

Given : Ratio of radii of two hemispheres = r1 : r2 = 3 : 5

To find : Ratio of curved surface areas = C1 : C2 = ?


Ratio of total surface areas = T1 : T2 = ?


Formula : CSA of hemisphere = 2r2


TSA of hemisphere = r2


Solution : CSA of first hemisphere = C1 = 2r12


CSA of second hemisphere = C2 = 2r22


⇒


TSA of first hemisphere = T1 = r12


TSA of second hemisphere = T2 = r22


⇒


∴ The ratio of the curved surface areas and total surface areas of the two solid hemispheres is 9 : 25 and 9 : 25 respectively.


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