If you double the radius of a sphere, its volume increases by what factor?
A. 8
B. 6
C. 2
D. 4
I thought maybe C.2 or D.4
V = (4/3)(pi)(r)^3
V = (4/3)(pi)(2r)^3
V = (4/3)(pi)8r^3
(4/3)(pi)(8)(r)^3 ÷ (4/3)(pi)(r)^3
Everything cancels out but the 8, so the answer is A.
To find out how the volume of a sphere changes when its radius is doubled, we can use the formula for the volume of a sphere: V = (4/3)πr^3, where V is the volume and r is the radius.
Let's consider a sphere with radius r. Its volume will be V = (4/3)πr^3.
Now, if we double the radius, the new radius will be 2r. So, the new volume will be V' = (4/3)π(2r)^3 = (4/3)π(8r^3) = (32/3)πr^3.
Now, let's compare the old volume to the new volume to determine the factor by which it increases:
V' / V = ((32/3)πr^3) / ((4/3)πr^3) = 32/4 = 8.
Therefore, when the radius of a sphere is doubled, its volume increases by a factor of 8.
So, the correct answer is A. 8.