Question

what is the approximate volume of the cone? use 3.14 for π. image of a green cone with height labeled 6 cm and radius labeled 5 cm options: 31.4 cm³, 157 cm³, 94.2 cm³, 471 cm³

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 \( r = 5 \, \text{cm} \) and the height \( h = 6 \, \text{cm} \). We are given \( \pi = 3.14 \).

Step3: Substitute the values into the formula

First, calculate \( r^2 \): \( r^2 = 5^2 = 25 \).
Then, calculate \( \pi r^2 \): \( 3.14\times25 = 78.5 \).
Next, multiply by \( h \): \( 78.5\times6 = 471 \).
Finally, multiply by \( \frac{1}{3} \): \( \frac{1}{3}\times471 = 157 \).

Answer:

\( 157 \, \text{cm}^3 \) (corresponding to the option "157 \( \text{cm}^3 \)")