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:
5^25105^31
125^3
To compare the volumes of the original sphere and the new sphere, we can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where r is the radius of the sphere.
Let's assume the radius of the original sphere is r.
The volume of the original sphere is:
Original sphere volume = (4/3)πr^3
The scale factor for the dilation is 5, so the radius of the new sphere is 5 times the radius of the original sphere: 5r.
The volume of the new sphere is:
New sphere volume = (4/3)π(5r)^3
Simplifying the equation, we have:
New sphere volume = (4/3)π(125r^3)
New sphere volume = (500/3)πr^3
Now, we can compare the volumes of the original and new sphere:
Original sphere volume x = New sphere volume
(4/3)πr^3 x = (500/3)πr^3
We can cancel out the π and r^3 on both sides of the equation, which leaves us with:
(4/3) = (500/3)
Therefore, the answer is:
original sphere volume x 5^25 = new sphere volume x 5^31