MarcJaynena
contestada

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

Respuesta :

I hope this helps you




C increased 2 times
JcAlmighty
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)

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

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