Question

problem a
this table shows the radiuses of four cones with a height of 18 meters.
complete the table with the volume of each cone.
(the table has columns: radius (m) with rows 1, 2, 3, 4; and volume (cu. m) with empty cells for each radius row)

Explanation:

The formula for 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. Given \( h = 18 \) meters, we can simplify the formula to \( V=\frac{1}{3}\pi r^{2}\times18 = 6\pi r^{2}\).

Step 1: For radius \( r = 1 \) m

Substitute \( r = 1 \) into the formula \( V = 6\pi r^{2} \).
\( V=6\pi\times(1)^{2}=6\pi\approx6\times3.14 = 18.84 \) cubic meters.

Step 2: For radius \( r = 2 \) m

Substitute \( r = 2 \) into the formula \( V = 6\pi r^{2} \).
\( V=6\pi\times(2)^{2}=6\pi\times4 = 24\pi\approx24\times3.14=75.36 \) cubic meters.

Step 3: For radius \( r = 3 \) m

Substitute \( r = 3 \) into the formula \( V = 6\pi r^{2} \).
\( V=6\pi\times(3)^{2}=6\pi\times9 = 54\pi\approx54\times3.14 = 169.56 \) cubic meters.

Step 4: For radius \( r = 4 \) m

Substitute \( r = 4 \) into the formula \( V = 6\pi r^{2} \).
\( V=6\pi\times(4)^{2}=6\pi\times16=96\pi\approx96\times3.14 = 301.44 \) cubic meters.

Answer:

Radius (m)	Volume (cu. m)
2	\( 24\pi\approx75.36 \)
3	\( 54\pi\approx169.56 \)
4	\( 96\pi\approx301.44 \)

(If we use \( \pi = 3.14 \), the approximate volumes are as shown in the table. If we leave \( \pi \) in the exact form, the volumes are \( 6\pi \), \( 24\pi \), \( 54\pi \), and \( 96\pi \) cubic meters respectively for radii 1, 2, 3, and 4 meters.)