Question

The volume of a cube is 1728 m3. What is the surface area of one face of the cube?

Answer 1

Answer:

56

Step-by-step explanation:

56 +78

-4556 so the answers is 56

mark me as brain

Answer 2

Hey comrade!

I need your attention here. Don't miss a point! :}

Answer:

144 Sq. meters

Step-by-step explanation:

We have a formula to calculate the volume of a cube according to which:-

$\boxed{\mathfrak{ \blue{volume \: of \: a \: cube = {side}^{3} } } }$

OR

$\boxed{ \mathfrak{ volume = side × side × side} }$

Let's see how we got this formula for finding the volume fo a cube.

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Why side³?

Imagine, you had a square sheet of side "n". so that it's surface area becomes "n²"

Now, if you pile up multiple such square sheets so that the height becomes equal to the length and breadth, i.e., “s” units.

can you see a cube forming?

Yeah! that's how a 2-dimensional object can be transformed to a 3-dimensional one.

A cube formed out of a square.

and since, volume is nothing but the space occupied by the cube it will be equal to n times the surface area of one sheet.

= n × (n²)

= n³

and n is the side of the cube

That's how we get volume of a cube = (side)³

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Calculating the side of the cube:

quickly applying the formula

volume of a cube = side³

1728 = side³

side = 12

(12 Is the cube root of 1728. so I wrote it straight away)

If you have the side of the cube, you have the key to your answer! :]

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Surface Area of one face of the cube:

It's asking for surface area of one face of the cube.

You must know that, a cube has six faces

[check the attachment]

Now, there are two ways to get to the final answer

METHOD I

(hard work)

calculate the surface area of the cube using the formula and divide it by six to get the surface area of one face

surface area of a cube = 6a²

= 6 × 12²

= 6 × 144

surface area of one face = 6/ 6 × 144

= 144 m²

METHOD II

(smart work)

Remember, when we formed a cube using "n" sided square sheets and piled them upto height n?

So, here we gotta find out the surface area of that square sheet used

( the area it covers on the surface it's being kept)

here n = 12

so area of the square sheet = 12² sq. m

= 144 Sq. m

and this is the area of one face of the cube.

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Also, remember that area of one face of the cube = side²

and don't use method 1 it's kinda absurd.