Question

The area of one face of cube is 289m^2. The volume of cube is

Answer 1

• The volume of the cube = 4913 m³

Given :

• The area of one face of a cube = 289 m².

To Find :

• The volume of the cube.

Solution :

First, we need to find the side of a cube.

Given,

The area of one face of a cube = 289 m²

We know that,

The face of a cube is a square.

That mean,

The area of a square = 289 m²

We know that,

Area of a square = a²

Where,

• a = side.

$: \implies \rm {a}^{2} = 289 \: {m}^{2} \\ \\ : \implies \rm a = \sqrt{289 \: {m}^{2} } \\ \\ : \implies \rm a = 17 \: m$

Hence, the length of the side of a cube is 17 m.

Now, we have to find the volume of the cube.

We know that,

Volume of cube = a³

Where,

• a = side = 17 m.

$: \implies \rm volume_{\sf {cube}} = {a}^{3} \\ \\ : \implies \rm volume_{\sf {cube}} = {(17 \: m)}^{3} \\ \\ : \implies \rm volume_{\sf {cube}} = 17 \times 17 \times 17 \: {m}^{3} \\ \\ : \implies \rm volume_{\sf {cube}} = 289 \times 17 \: {m}^{3} \\ \\ : \implies \rm volume_{\sf {cube}} = 4913 \: {m}^{3}$

Hence,

The volume of the cube is 4913 m³

Answer 2

Answer:

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ᴀʀᴇᴀ ᴏꜰ ᴏɴᴇ ꜰᴀᴄᴇ ᴏꜰ ᴄᴜʙᴇ=64ᴍ2

ʟᴇᴛ ꜱɪᴅᴇ ᴏꜰ ᴄᴜʙᴇ=xᴍ

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴩʀᴏʙʟᴇᴍ,

x2=64

x=64

x=8

∴ ꜱɪᴅᴇ ᴏꜰ ᴄᴜʙᴇ=8ᴍ

ᴠᴏʟᴜᴍᴇ ᴏꜰ ᴄᴜʙᴇ=(ꜱɪᴅᴇ)3

=(8)3

=512ᴍ3

∴ ᴠᴏʟᴜᴍᴇ ᴏꜰ ᴄᴜʙᴇ=512ᴍ³