Archive
14th of March 2017
Mathematics
Q:

1.a sphere and a cube have equal surface areas. then find ratioof the volume of the sphere to that of cube

Priya Dharshini - CBSE - Class X

Tuesday, March 14, 2017 at 17:56:PM

A:

begin mathsize 16px style space As space the space surface space area space of space sphere space is space equal space to space that space of space cube space
rightwards double arrow 4 πr squared equals 6 straight a squared
rightwards double arrow straight r squared over straight a squared equals space fraction numerator 6 over denominator 4 straight pi end fraction
space rightwards double arrow straight r over straight a equals space fraction numerator square root of 6 over denominator 2 square root of straight pi end fraction space space space
The space ratio space of space the space vloume space of space sphere space to space cube space is space
equals space fraction numerator fraction numerator 4 straight pi space straight r cubed over denominator 3 end fraction over denominator space straight a cubed end fraction space equals space fraction numerator 4 straight pi space straight r cubed over denominator space 3 straight a cubed end fraction equals space fraction numerator 4 straight pi over denominator space 3 end fraction fraction numerator space straight r cubed over denominator space straight a cubed end fraction equals space fraction numerator 4 straight pi over denominator space 3 end fraction open parentheses fraction numerator space straight r over denominator space straight a end fraction close parentheses cubed space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
Putting space the space value space of space eq space 1 space comma space we space get space
fraction numerator vol space of space sphere over denominator vol space of space cube end fraction equals space fraction numerator 4 straight pi over denominator space 3 end fraction open parentheses fraction numerator square root of 6 over denominator 2 square root of straight pi end fraction close parentheses cubed equals space fraction numerator 4 straight pi over denominator space 3 end fraction fraction numerator 6 square root of 6 over denominator space 8 straight pi square root of straight pi end fraction equals fraction numerator square root of 6 over denominator square root of straight pi space end fraction
end style

Tuesday, March 14, 2017 at 18:15:PM