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

Question

asked Jul 22, 2019 170k views

1 Answer

Slymore · Answer 1 · 2019-07-28T09:18:17+0000

Answer:

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