Question

find the volume of the specified cone. use 3.14 for π, and round your answer to the nearest whole number.
diameter = 3 cm, height = 4 cm
a. 57 cu. cm
b. 25 cu. cm
c. 38 cu. cm
d. 9 cu. cm

please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Find the radius

The diameter is 3 cm, so the radius \( r=\frac{d}{2}=\frac{3}{2} = 1.5\) cm.

Step2: Recall the volume formula for a cone

The volume \( V\) of a cone is given by \( V=\frac{1}{3}\pi r^{2}h\).

Step3: Substitute the values

We know \( \pi = 3.14\), \( r = 1.5\) cm, and \( h = 4\) cm. Substitute these into the formula:
\( V=\frac{1}{3}\times3.14\times(1.5)^{2}\times4\)
First, calculate \( (1.5)^{2}=2.25\). Then:
\( V=\frac{1}{3}\times3.14\times2.25\times4\)
\( \frac{1}{3}\times3.14\times2.25 = 3.14\times0.75=2.355\)
Then, \( 2.355\times4 = 9.42\approx9\) (rounded to the nearest whole number). Wait, no, wait, let's recalculate:
Wait, \( \frac{1}{3}\times3.14\times(1.5)^2\times4=\frac{1}{3}\times3.14\times2.25\times4\)
\( 3.14\times2.25 = 7.065\), \( 7.065\times4=28.26\), \( \frac{28.26}{3}=9.42\approx9\)? Wait, no, I made a mistake earlier. Wait, \( (1.5)^2 = 2.25\), \( 3.14\times2.25 = 7.065\), \( 7.065\times4 = 28.26\), then divide by 3: \( 28.26\div3 = 9.42\), which rounds to 9. So the volume is approximately 9 cubic centimeters.

Answer:

D. 9 cu. cm