A sphere is dilated by a scale factor of 5 to create a new sphere. (This means the new sphere is 5 times as big as the original!)
The volume of the new sphere compares with the volume of the original sphere: original sphere volume x ________ = new sphere volume.
Word Bank:
10 5 5^3 5^2 1
Blank 1:
btw izuku the fast answer is an ai, a robot, the person who programmed it was rly smart but the person with the fast answer/ the bot probably doesnt care
5^3
Thank you so much for the fast answer; I greatly appreciate it!
it’s just 5 I think
Oh okay thank
To find the comparison factor, we need to determine how the volume of a sphere changes when it is dilated by a certain scale factor. The volume of a sphere is given by the formula V = (4/3) π r^3, where r is the radius.
In this case, the scale factor is 5, which means the radius of the new sphere is 5 times larger than the radius of the original sphere.
Let's assume the original sphere has a radius of r. Therefore, the radius of the new sphere is 5r.
Now, let's calculate the volume of the original sphere:
V_original = (4/3) π r^3
Next, we need to find the volume of the new sphere:
V_new = (4/3) π (5r)^3
To simplify this expression, we can use the fact that (a^b)^c = a^(b*c):
V_new = (4/3) π 5^3 r^3
Now, we have the volume of the new sphere in terms of the original sphere's radius.
Comparing the two volumes, we can express the comparison factor as:
original sphere volume x (5^3) = new sphere volume
Therefore, the answer for Blank 1 is 5^3.