Question

the volume of this cone is 9,696.79728 cubic centimeters. what is the height of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 17.4 cm h ≈ centimeters submit

Explanation:

Step1: Recall the volume formula for 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 of the base and \( h \) is the height of the cone. We are given that \( V = 9696.79728\space cm^{3}\), \( r=17.4\space cm \) and \( \pi\approx3.14 \). We need to solve for \( h \). First, we can rearrange the formula for \( h \):

From \( V=\frac{1}{3}\pi r^{2}h \), multiply both sides by 3: \( 3V=\pi r^{2}h \). Then divide both sides by \( \pi r^{2} \) to get \( h=\frac{3V}{\pi r^{2}} \).

Step2: Substitute the given values into the formula

Substitute \( V = 9696.79728 \), \( \pi = 3.14 \) and \( r = 17.4 \) into the formula for \( h \):

First, calculate \( r^{2} \): \( r^{2}=(17.4)^{2}=17.4\times17.4 = 302.76 \)

Then, calculate \( \pi r^{2} \): \( 3.14\times302.76=3.14\times302.76 = 949.6664 \)

Next, calculate \( 3V \): \( 3\times9696.79728 = 29090.39184 \)

Now, calculate \( h \) by dividing \( 3V \) by \( \pi r^{2} \): \( h=\frac{29090.39184}{949.6664} \)

Step3: Perform the division

\( \frac{29090.39184}{949.6664}=30.63 \) (rounded to the nearest hundredth)

Answer:

\( 30.63 \)