how to find the total volume of 15 cube whose edges are 16 cm , 17cm, 18cm, 19cm ......30cm respectively
it is a tenth standard portion in lesson 2 nd. exercise sum 2.6 ( 6th sum )
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actually this is 11th class question find in your textbook
we know ,
1^3+2^3+3^3+4^3+.........n^3={n (n+1)/2}^2
now use this ,
total volume of cubes =16^3+17^3+18^3+.........30^3
also we write this ,
=(1^3+2^3+3^3+4^3+....30^3)-(1^3+2^3+3^3+......+15^3)
={30 x 31/2}^2-{15 x 16/2}^2
=(15 x 31)^2-(15x 8)^2
=15^2 {31^2-8^2}=225 x 23 x39 cm^3
we know ,
1^3+2^3+3^3+4^3+.........n^3={n (n+1)/2}^2
now use this ,
total volume of cubes =16^3+17^3+18^3+.........30^3
also we write this ,
=(1^3+2^3+3^3+4^3+....30^3)-(1^3+2^3+3^3+......+15^3)
={30 x 31/2}^2-{15 x 16/2}^2
=(15 x 31)^2-(15x 8)^2
=15^2 {31^2-8^2}=225 x 23 x39 cm^3
kiruthik2003:
thank u so much my frnd
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