Question

a cone has a height of 18 centimeters and a radius of 7 centimeters. what is its volume? round your answer to the nearest hundredth. 230.79 461.58 923.16 1846.32 what is the volume of this cone? round your answer to the nearest hundredth. (image of a cone with height 15 yd and radius 4 yd) 502.40 251.20 62.80 125.60

Explanation:

First Sub - Question (Cone with height 18 cm and radius 7 cm)

Step 1: 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 and \( h \) is the height.

Step 2: Substitute the given values

We are given that \( r = 7\) cm and \( h=18\) cm. Substituting these values into the formula, we get \( V=\frac{1}{3}\times\pi\times(7)^{2}\times18\).
First, calculate \( 7^{2}=49 \), then \( 49\times18 = 882 \). Then, \( \frac{1}{3}\times882=294 \). So, \( V = 294\pi\).

Step 3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V=294\times3.14159\approx923.16 \) (rounded to the nearest hundredth).

Second Sub - Question (Cone with height 15 yd and radius 4 yd)

Step 1: Recall the volume formula for a cone

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.

Step 2: Substitute the given values

We have \( r = 4\) yd and \( h = 15\) yd. Substituting into the formula, \( V=\frac{1}{3}\times\pi\times(4)^{2}\times15\).
First, calculate \( 4^{2}=16 \), then \( 16\times15 = 240 \). Then, \( \frac{1}{3}\times240 = 80 \). So, \( V=80\pi\).

Step 3: Calculate the numerical value

Using \( \pi\approx3.14 \), we get \( V = 80\times3.14=251.20 \) (rounded to the nearest hundredth).

Answer:

First Sub - Question: 923.16
Second Sub - Question: 251.20