Question

1. a spheres radius is tripled. how does its volume change?

a. the volume increases by six times.
b. the volume triples.
c. the volume doubles.
d. the volume increases by 27 times.

Explanation:

Step1: Recall the volume formula of a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\), where \(r\) is the radius of the sphere.

Step2: Calculate the new volume when the radius is tripled

Let the original radius be \(r\), and the new radius be \(R = 3r\). The new volume \(V'=\frac{4}{3}\pi R^{3}\). Substitute \(R = 3r\) into the formula: \(V'=\frac{4}{3}\pi(3r)^{3}=\frac{4}{3}\pi\times27r^{3}=27\times\frac{4}{3}\pi r^{3}\). Since \(V=\frac{4}{3}\pi r^{3}\), we have \(V' = 27V\).

Answer:

d. The volume increases by 27 times.