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Calculate the volume of a CONE with a height of 6 inches and a diameter of 6 inches.
Give your answer both in terms of
pi and by using 3.14 to approximate
pi.

In terms of
pi
Volume

Using 3.14 as an approximate

Calculate the volume of a CONE with a height of $6$ inches and a diameter of $6$ inches. $\newline$ Give your answer both in terms of $\pi$ and by using $3$ . $14$ to approximate $\pi$ . $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline In terms of $\pi$ & Volume \\ $\newline$ \hline Using $3$ . $14$ as an approximate & \\ $\newline$ \hline $\newline$ \end{tabular}

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Volume of cylinders

Full solution

Q. Calculate the volume of a CONE with a height of

6

inches and a diameter of

6

inches.

\newline

Give your answer both in terms of

\pi

and by using

3

.

14

to approximate

\pi

.

\newline

\begin{tabular}{|c|c|}

\newline

\hline In terms of

\pi

& Volume \\

\newline

\hline Using

3

.

14

as an approximate & \\

\newline

\hline

\newline

\end{tabular}

Identify Formula and Values: Identify the formula for the volume of a cone and the given values. $\newline$ 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 of the cone. $\newline$ Given values: Height ( $h$ ) = $6$ inches, Diameter = $6$ inches. $\newline$ To find the radius, we divide the diameter by $2$ . Radius ( $r$ ) = Diameter / $2$ = $6$ inches / $2$ = $r$ $1$ inches.
Calculate Volume in Terms of π: Plug the values into the formula to calculate the volume in terms of π. $\newline$ Volume $V = \frac{1}{3}\pi r^2h$ $\newline$ $V = \frac{1}{3}\pi(3 \text{ inches})^2(6 \text{ inches})$ $\newline$ $V = \frac{1}{3}\pi(9 \text{ inches}^2)(6 \text{ inches})$ $\newline$ $V = \frac{1}{3}\pi(54 \text{ inches}^3)$ $\newline$ $V = 18\pi \text{ inches}^3$
Calculate Volume Numerically: Use $3.14$ as an approximation for $\pi$ to calculate the volume numerically. $\newline$ $V \approx (1/3)(3.14)(3 \text{ inches})^2(6 \text{ inches})$ $\newline$ $V \approx (1/3)(3.14)(9 \text{ inches}^2)(6 \text{ inches})$ $\newline$ $V \approx (1/3)(3.14)(54 \text{ inches}^3)$ $\newline$ $V \approx (1/3)(169.56 \text{ inches}^3)$ $\newline$ $V \approx 56.52 \text{ inches}^3$

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\newline

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\newline

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\newline

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\newline

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