Find the volume of a right circular cone that has a height of $9.5 \mathrm{~cm}$ and a base with a circumference of $9 \mathrm{~cm}$ . Round your answer to the nearest tenth of a cubic centimeter. $\newline$ Answer: $\mathrm{cm}^{3}$

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Q. Find the volume of a right circular cone that has a height of

9.5 \mathrm{~cm}

and a base with a circumference of

9 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

Answer:

\mathrm{cm}^{3}

Volume Formula for Cone: To find the volume of a cone, we need to know the radius of the base and the height. The formula for the volume of a cone is $V = (\frac{1}{3})\pi r^2 h$ , where $r$ is the radius and $h$ is the height. We are given the height as $9.5$ cm, but we need to find the radius from the circumference of the base.
Calculate Radius from Circumference: The circumference of a circle is given by the formula $C = 2\pi r$ , where $C$ is the circumference and $r$ is the radius. We can rearrange this formula to solve for the radius: $r = \frac{C}{2\pi}$ . The circumference is given as $9$ cm.
Calculate Volume with Radius and Height: Now we calculate the radius: $r = \frac{9 \, \text{cm}}{(2\pi)}$ . Using $\pi \approx 3.14159$ , we get $r \approx \frac{9 \, \text{cm}}{(2 \times 3.14159)} \approx \frac{9 \, \text{cm}}{6.28318} \approx 1.432 \, \text{cm}$ .
Perform Calculation: With the radius found, we can now calculate the volume of the cone using the volume formula $V = \frac{1}{3}\pi r^2h$ . Substituting the values we have $r \approx 1.432$ cm and $h = 9.5$ cm, we get $V \approx \frac{1}{3} \times 3.14159 \times (1.432\,\text{cm})^2 \times 9.5\,\text{cm}$ .
Round to Nearest Tenth: Performing the calculation: $V \approx (1/3) \times 3.14159 \times (1.432 \, \text{cm})^2 \times 9.5 \, \text{cm} \approx (1/3) \times 3.14159 \times 2.049824 \times 9.5 \, \text{cm} \approx 20.431 \, \text{cm}^3$ .
Final Volume: Finally, we round the answer to the nearest tenth of a cubic centimeter. The volume of the cone is approximately $20.4\,\text{cm}^3$ .