Question

the volume of a sphere depends on the cube of its:
a. diameter
b. height
c. radius
d. circumference
a cylinder has a radius of 5 cm and a height of 10 cm. what is its volume in terms of π?
a. 150π
b. 100π
c. 250π
d. 500π

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. So the volume of a sphere depends on the cube of its radius.

Step2: Recall the volume formula of a cylinder

The volume formula of a cylinder is \(V = \pi r^{2}h\). Given \(r = 5\space cm\) and \(h=10\space cm\).

Step3: Substitute the values into the formula

Substitute \(r = 5\) and \(h = 10\) into \(V=\pi r^{2}h\), we get \(V=\pi\times5^{2}\times10\).

Step4: Calculate the result

First, \(5^{2}=25\), then \(25\times10 = 250\). So \(V = 250\pi\space cm^{3}\).

Answer:

1. C. Radius
2. C. \(250\pi\)