Doubling radius?
"The diameter of a sphere is doubled. State the factor by which the volume changes."
Can someone please help me with a solution? Thanks.
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Write the formula for the volume. There’s a radius in it. Then you set for the radius in the formula 2r. Then look what happens to the two and you have your factor.
Volume goes with the third potency of the radius – with a doubling of the radius, the volume of a sphere increases…
The volume increases.
If you change the scale, it changes
Volume with the third potency. We double here,
and what is the third potency of 2?
You can also use the formula:
V = 4/3*pi*r3
Now, instead of 2r, you’re using:
V = 4/3*pi*(2r)3
How did V change now?