Question

If a sphere’s volume is doubled, what is the corresponding change in its radius?

A.
The radius is increased to 20 times the original size.
B.
The radius is increased to 4 times the original size.
C.
The radius is increased to 2 times the original size.
D.
The radius is increased to 8 times the original size

Answer 1

I hope this helps you




C increased 2 times

Answer 2

The answer is ∛2 times.

The volume (V) of the sphere with radius r is: V = 4/3 * π r³
Let's express it in the term of r:
V = 4/3 * π r³
r³ = 3/4 * V/π
r = ∛(3/4 * V/π)

Now, after doubling the volume of the square: 2V1 = 4/3 * π r1³
Let's express it in the term of r1:
2V = 4/3 * π r1³
r1³ = 3/4 * 2V/π
r1³ = 3/2V/π
r1 = ∛(3/2 * V/π)


`(r1)/(r) = \frac{ \sqrt[3]{ (3)/(2) * (V)/( \pi ) } }{\sqrt[3]{ (3)/(4) * (V)/( \pi ) }} = \sqrt[3]{ ((3)/(2)*(V)/( \pi ) )/((3)/(4)*(V)/( \pi ) ) } =\sqrt[3]{ ((3)/(2) )/((3)/(4) ) } = \sqrt[3]{ (3)/(2) * (4)/(3) } = \sqrt[3]{2}`