Question

if a cone has a radius of 5 cm and a height of 10 cm, its volume is:
a. $\frac{50}{3}pi cm^{3}$
b. $\frac{250}{3}pi cm^{3}$
c. $250pi cm^{3}$
d. $25pi cm^{3}$

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume \(V\) of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 5\ \text{cm}\) and \(h=10\ \text{cm}\). Substitute these into the formula: \(V=\frac{1}{3}\pi\times(5)^{2}\times10\).

Step3: Calculate the value

First, calculate \((5)^{2}=25\). Then \(V=\frac{1}{3}\pi\times25\times 10=\frac{250}{3}\pi\ \text{cm}^3\).

Answer:

B. \(\frac{250}{3}\pi\ \text{cm}^3\)