If all the dimensions of a cube are increased by 5 units, how will the surface area change?
increase by a factor of 5
increase by a factor of 10
increase by a factor of 25
increase by a factor of 50
area of one side of cube =
(x+5)^2 = x^2 + 10 x + 25 = not something times original
I think you mean increase lengths by a FACTOR of five.
5^2 = 25
To find out how the surface area of a cube changes when all its dimensions are increased by 5 units, we need to understand the formula for the surface area of a cube.
The surface area of a cube is given by the formula: SA = 6 * (side)^2.
Let's assume that the side length of the original cube is "s".
When all dimensions are increased by 5 units, the new side length becomes s + 5.
So, the surface area of the new cube is given by: SA_new = 6 * (s + 5)^2.
To determine how the surface area changes, we can compare the original surface area (SA) with the new surface area (SA_new).
SA_new = 6 * (s + 5)^2
Dividing the new surface area by the original surface area gives us:
SA_new / SA = (6 * (s + 5)^2) / (6 * s^2)
Canceling out the common factors of 6, we get:
SA_new / SA = ((s + 5)^2) / (s^2)
Expanding the numerator and denominator further, we have:
SA_new / SA = (s^2 + 10s + 25) / (s^2)
Since we are interested in finding how the surface area changes, we need to determine the ratio of the new surface area to the original surface area.
When we simplify this ratio, we get:
SA_new / SA = 1 + (10s + 25) / (s^2)
Now, we can analyze the options provided:
a) increase by a factor of 5
b) increase by a factor of 10
c) increase by a factor of 25
d) increase by a factor of 50
To determine which option is correct, we need to substitute different values for "s" into our simplified ratio and see how it changes.
For example, let's assume that "s" is equal to 1.
Substituting this value into our simplified ratio, we get:
SA_new / SA = 1 + (10 * 1 + 25) / (1^2)
= 1 + (10 + 25) / 1
= 1 + 35
Here, we can see that the simplified ratio is equal to 36.
Now, let's try another value of "s," such as 2.
SA_new / SA = 1 + (10 * 2 + 25) / (2^2)
= 1 + (20 + 25) / 4
= 1 + 45 / 4
In this case, we can see that the simplified ratio is equal to 12.25.
Similarly, if we substitute other values for "s" into the simplified ratio, we will find that it varies depending on the side length of the cube.
Therefore, we cannot conclude that the surface area will increase by a factor of 5, 10, 25, or 50. The change in surface area depends on the side length of the cube.