Question

problem 4
this table shows the radiuses of four cones with a height of 18 meters.
complete the table with the volume of each cone
radius (m)
1
2
3
4
volume (cu. m)

Explanation:

Step1: Recall cone volume formula

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$, where $h=18$ m. Substitute $h$:
$V = \frac{1}{3}\pi r^2 (18) = 6\pi r^2$

Step2: Calculate for $r=1$ m

Substitute $r=1$ into the formula:
$V = 6\pi (1)^2 = 6\pi \approx 18.85$

Step3: Calculate for $r=2$ m

Substitute $r=2$ into the formula:
$V = 6\pi (2)^2 = 6\pi(4) = 24\pi \approx 75.40$

Step4: Calculate for $r=3$ m

Substitute $r=3$ into the formula:
$V = 6\pi (3)^2 = 6\pi(9) = 54\pi \approx 169.65$

Step5: Calculate for $r=4$ m

Substitute $r=4$ into the formula:
$V = 6\pi (4)^2 = 6\pi(16) = 96\pi \approx 301.59$

Answer:

Radius (m)	Volume (cu. m)
2	$24\pi$ (≈75.40)
3	$54\pi$ (≈169.65)
4	$96\pi$ (≈301.59)