Question

If the length of each diagonal of a cube is doubled, then what is the change in it's volume?​

Answer 1

Solution:- volume of cube= √3d^3/9

if we double the length of diagonal it becomes,

2√3d^3/9

Hence, the volume become double...

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Answer 2

The volume of the cube increases 8 times.

Step-by-step explanation:

The length of each diagonal of cube is doubled.

Let d be the length of diagonal.

Volume of cube =

$V = \dfrac{d^3}{3\sqrt3}$

New length of diagonal

d' = 2d

New volume of cube =

$V' = \dfrac{(2d)^3}{3\sqrt3}\\\\V' = \dfrac{8d^3}{3\sqrt3}\\\\V' = 8V$

Thus, the volume of the cube increases 8 times.

#LearnMore

What is the change in the volume of the cube if the length is doubled.​

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