Question

By what percent the volume of a cube increases if length of each edge is increased by 50 percent

Answer 1

Answer:337.5%

Step-by-step explanation:

We know,

Volume of cube=l^3

Now when l is increased by 50 % then l'=l+50% of l

=I+(l/2)=3l/2

Now volume with increased length will be

V'=(l')^3=(3l/2)^3=27l^3/8=3.375l^3

Therefore % increase in volume=(V'/V)×100%

=3.375×100%=337.5%

Answer 2

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As we know length of each side of cube is equal.

so, volume of cube = a^3

now , if length is increased by 50%

new length = a + a/2

= 3a/2

New volume = (3a/2)^3

=> 27a^3/8

now, % increase in volume will be

[(new volume - old volume)/new volume ] *100

=>( 19/8)÷27/8*100

=> 2.375/3.3 *100

= 71%