Question

How long is the edge of a cube whose volume is twice that of the cube below? Round to the nearest tenth.

Answer 1

`\large\boxed{10.1\ cm}`

Explanation:

The formula of a volume of a cube:

`V=a^2`

a - length of the edge

We have a = 8cm. Substitute:

`V=8^3=512\ cm^3`

The volume of second cube:

`V'=2V\to V'=2(512\ cm^3)=1024\ cm^3`

The length of the edge of the second cube (b):

`b^3=1024\to b=\sqrt[3]{1024}\ cm^3`

`1024=2^(10)=2^(9+1)=2^9\cdot2`

Used
`a^n\cdot a^m=a^(n+m)`

`b=\sqrt[3]{1024}=\sqrt[3]{2^(10)}=\sqrt[3]{2^9\cdot2}=\sqrt[3]{2^9}\cdot\sqrt[3]{2}`

Use
`(a^n)^m=a^(nm)`

`=\sqrt[3]{2^(3\cdot3)}\cdot\sqrt[3]{2}=\sqrt[3]{(2^3)^3}\cdot\sqrt[3]{2}`

Use
`\sqrt[3]{a^3}=a`

`=2^3\sqrt[3]{2}=8\sqrt[3]{2}\ cm`

`\sqrt[3]{2}\approx1.26\to b\approx8(1.26)\approx10.1\ cm`

Other method:

`V'=2V\\\\V=a^3,\ V'=b^3\to b^3=2a^3\to b=\sqrt[3]{2a^3}\\\\b=a\sqrt[3]2`

`a=8\ cm\to b=8\sqrt[3]2\ cm\approx10.1\ cm`