Question

b. the height of a cone is 15 cm. the diameter of the cone is 10 cm. find the volume of the cone. round to the nearest hundredth of a cubic centimeter.

Explanation:

Step1: Recall the formula for the volume of a cone

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

Step2: Find the radius of the cone

We know that the diameter \( d = 10\space\text{cm} \), and the radius \( r=\frac{d}{2} \). So \( r=\frac{10}{2}=5\space\text{cm} \).

Step3: Substitute the values of \( r \) and \( h \) into the volume formula

We are given \( h = 15\space\text{cm} \), \( r = 5\space\text{cm} \). Substituting into \( V=\frac{1}{3}\pi r^{2}h \), we get \( V=\frac{1}{3}\times\pi\times(5)^{2}\times15 \).
First, calculate \( (5)^{2}=25 \), then \( \frac{1}{3}\times25\times15 = 25\times5=125 \). So \( V = 125\pi\space\text{cubic centimeters} \).

Step4: Calculate the numerical value and round to the nearest hundredth

Using \( \pi\approx3.14159 \), we have \( V\approx125\times3.14159 = 392.69875 \). Rounding to the nearest hundredth, we look at the thousandth place digit which is 8. Since \( 8>5 \), we round up the hundredth place. So \( 392.69875\approx392.70 \).

Answer:

\( 392.70 \) cubic centimeters