Question

what is the volume of this cone? round your answer to the nearest hundredth. 69 cm 126 cm cubic centimeters submit

Explanation:

Step1: Find the radius of the cone

The diameter of the cone is 126 cm, so the radius \( r=\frac{126}{2}=63 \) cm.

Step2: Recall the formula for the volume of 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. Here, \( r = 63 \) cm and \( h=69 \) cm.

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times\pi\times(63)^{2}\times69 \)
First, calculate \( 63^{2}=63\times63 = 3969 \)
Then, \( \frac{1}{3}\times3969\times69=3969\times23 = 91287 \)
So, \( V = 91287\times\pi \)

Step4: Calculate the numerical value

\( V\approx91287\times3.1415926535\approx286733.43 \) (rounded to the nearest hundredth)

Answer:

\( 286733.43 \)