sof-IMO 2014

Geometry Level 2

Let A and B be 2 solid spheres such that the surface area of B is 300% higher (means 300 % more) than that of A. The volume of A is found to be K% lower than the volume of B. The value of K must be

92.5 90.5 87.5 85.5

Manish Mayank by Manish Mayank , 20, India

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2 solutions

Tanmay Goyal
Jan 27, 2015

NICE !...bt pretty easy ...

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Nelson Mandela
Dec 31, 2014

Let a be radius of smaller sphere and b be the radius of larger sphere. as surface area is 4pi r^2, so the surface area of the smaller sphere is 4pi a^2 and surface area of larger square is 4pi b^2. then, as 4pi b^2 = 4 x 4pi a^2( 1+300/100=1+3=4) so b^2=4a^2 then, b=2a. now, volume of smaller sphere is 4/3 pi a^3. volume of larger sphere is 4/3 pi b^3=4/3 pi (2a)^3=8 x 4/3 pi a^3. thus, volume of larger sphere is 8 times the larger sphere. hence, percentage decrease is (8-1)/8 x 100 =7/8 x 100 =87.5%

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@Manish Mayank I think it is better to say SOF IMO because I think it can be misinterpreted for the "real" IMO.

milind prabhu - 6 years, 4 months ago

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