Question

The surface area of a cube is 18 3/8 m square. Find its volume.

Answer 1

`5(23)/(64)\approx 5.36` cubic meters.

Explanation:

We have been given that the surface area of a cube is
`18(3)/(8)` square meters and we are asked to find the volume of the cube.

Since we know that surface area of a cube with each edge equals a units is:

`\text{Total surface area of cube}=6a^2`

Let us find length of each edge using surface area formula.

`18(3)/(8)=6a^2`

Let us convert our given area into mixed fraction.

`(147)/(8)=6a^2`

Upon dividing both sides of our equation by 6 we will get,

`(147)/(8*6)=a^2`

`(147)/(48)=a^2`

Upon taking square root of both sides we will get,

`(7√(3))/(4√(3))=a`

`(7)/(4)=a`

Now we will use volume of cube formula with each side length 'a'.

`\text{Volume of cube}=a^3`

`\text{Volume of cube}=((7)/(4))^3`

`\text{Volume of cube}=(343)/(64)`

`\text{Volume of cube}=5(23)/(64)`

`\text{Volume of cube}=5.359375\approx 5.36`

Therefore, the volume of cube will be
`5(23)/(64)` cubic meters.