Express the surface area of a cube

In summary, the surface area of a cube can be found using the formula 6s<sup>2</sup>, where s is the length of one side of the cube. It can also be expressed in terms of its volume by using the formula 6√(V/6), where V is the volume of the cube. An example of finding the surface area of a cube is using a cube with a side length of 5 cm, which would result in a surface area of 150 square centimeters. There is also a shortcut method of simply multiplying the length of one side by itself and then by 6. The surface area of a cube cannot be negative as it is a measurement of area and negative numbers do not
  • #1
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Homework Statement


Express the surface area of a cube as a function of its volume.


Homework Equations


Cubic Volume=Length x Width x Height (V=Length of side^3)
Cubic Surface Area= (Length of side^2)x6

The Attempt at a Solution


f(V)=(X^3/X) x 6...sorry, I don't know if I'm on the right track, as there are no given examples similar to this in my text.
 
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  • #2
Maybe solve V=L^3 for L in terms of V and then substitute into A=6*L^2?
 
  • #3


Your attempt is a good start, but there are a few errors. First, the surface area of a cube is not equal to its volume. The surface area is the sum of all of its sides, while the volume is the amount of space inside the cube. Secondly, your equation for surface area is incorrect. It should be (length of side)^2 x 6, not (length of side^2) x 6. This is because the surface area of a cube is calculated by finding the area of one side (length x width) and then multiplying it by the number of sides (6).

To express the surface area of a cube as a function of its volume, we first need to find the length of one side in terms of the volume. This can be done by taking the cube root of the volume, since the volume of a cube is equal to (length of side)^3. So, the length of one side would be equal to the cube root of the volume.

Now, to find the surface area, we can plug this expression for the length of one side into the equation for surface area:

Surface area = ((cube root of volume)^2) x 6

This can also be written as a function:

f(V) = ((V^(1/3))^2) x 6

So, for any given volume, we can use this function to calculate the surface area of the cube.
 

1. What is the formula for finding the surface area of a cube?

The formula for finding the surface area of a cube is 6s2, where s is the length of one side of the cube.

2. How do you express the surface area of a cube in terms of its volume?

The surface area of a cube can be expressed in terms of its volume by using the formula 6√(V/6), where V is the volume of the cube.

3. Can you explain how to calculate the surface area of a cube with an example?

Sure, let's say we have a cube with side length of 5 cm. To find the surface area, we would use the formula 6(5cm)2, which simplifies to 150 cm2. This means that the surface area of the cube is 150 square centimeters.

4. Is there a shortcut method for finding the surface area of a cube?

Yes, there is a shortcut method for finding the surface area of a cube. You can simply multiply the length of one side by itself, and then multiply that result by 6. This will give you the same answer as using the formula 6s2.

5. Can the surface area of a cube be negative?

No, the surface area of a cube cannot be negative. Since surface area is a measurement of area, it cannot have a negative value. Negative numbers are used to represent quantities less than zero, which does not apply to the concept of surface area.

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