Question

what is the volume of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. (cone diagram with height 42 in, radius 24 in) blank cubic inches

Explanation:

Step1: 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 of the base and \( h \) is the height of the cone.

Step2: Identify the values of \( r \) and \( h \)

From the diagram, the radius \( r = 24 \) inches and the height \( h = 42 \) inches. We are also given that \( \pi \approx 3.14 \).

Step3: Substitute the values into the formula

First, calculate \( r^2 \): \( r^2 = 24^2 = 576 \).
Then, substitute \( \pi \approx 3.14 \), \( r^2 = 576 \), and \( h = 42 \) into the volume formula:
\( V=\frac{1}{3}\times3.14\times576\times42 \)

Step4: Perform the calculations

First, calculate \( \frac{1}{3}\times576 = 192 \).
Then, calculate \( 192\times42 = 8064 \).
Then, calculate \( 3.14\times8064 \):
\( 3.14\times8064 = 25320.96 \)

Answer:

25320.96