Question

1. if a cone has a radius of 5 cm and a height of 10 cm, its volume is:

a. \\( \frac { 50 } { 3 } \pi \mathrm { cm } ^ { 3 } \\)
b. \\( \frac { 250 } { 3 } \pi \mathrm { cm } ^ { 3 } \\)
c. \\( 250 \pi \mathrm { cm } ^ { 3 } \\)
d. \\( 25 \pi \mathrm { cm } ^ { 3 } \\)

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for 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 $r = 5\mathrm{cm}$ and $h=10\mathrm{cm}$, we substitute into the formula: $V=\frac{1}{3}\pi\times(5)^{2}\times10$.

Step3: Calculate the value

First, calculate $(5)^{2}=25$. Then, $25\times10 = 250$. So, $V=\frac{1}{3}\pi\times250=\frac{250}{3}\pi\mathrm{cm}^3$.

Answer:

B. $\frac{250}{3}\pi\mathrm{cm}^3$