Questions: The volume of a right circular cylinder can be approximated as follows: Volume = π r^2 h, where r is the radius of the cylinder and h is the height of the cylinder; π is a constant that is roughly equal to 3. Using the simple approximation above, calculate the volume of a right circular cylinder with a radius of 2 meters and a height of 7 meters. A. 42 m^3 B. 12 m^3 C. 168 m^3 D. 84 m^3

The volume of a right circular cylinder can be approximated as follows: Volume = π r^2 h, where r is the radius of the cylinder and h is the height of the cylinder; π is a constant that is roughly equal to 3. Using the simple approximation above, calculate the volume of a right circular cylinder with a radius of 2 meters and a height of 7 meters. A. 42 m^3 B. 12 m^3 C. 168 m^3 D. 84 m^3
Transcript text: The volume of a right circular cylinder can be approximated as follows: Volume $=\pi r^{2} h$, where $r$ is the radius of the cylinder and $h$ is the height of the cylinder; $\pi$ is a constant that is roughly equal to 3 . Using the simple approximation above, calculate the volume of a right circular cylinder with a radius of 2 meters and a height of 7 meters. A. $42 \mathrm{~m}^{3}$ B. $12 \mathrm{~m}^{3}$ C. $168 \mathrm{~m}^{3}$ D. $84 \mathrm{~m}^{3}$
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Solution

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Solution Steps

To calculate the volume of a right circular cylinder, use the formula \( \text{Volume} = \pi r^2 h \). Here, \( r = 2 \) meters and \( h = 7 \) meters. Substitute these values into the formula and use \( \pi \approx 3 \) to approximate the volume.

Step 1: Given Values

We are given the radius \( r = 2 \, \text{m} \) and the height \( h = 7 \, \text{m} \) of the right circular cylinder. We will use the approximation \( \pi \approx 3 \).

Step 2: Volume Formula

The volume \( V \) of a right circular cylinder is calculated using the formula: \[ V = \pi r^2 h \]

Step 3: Substitute Values

Substituting the given values into the formula: \[ V = 3 \cdot (2)^2 \cdot 7 \]

Step 4: Calculate Volume

Calculating the expression: \[ V = 3 \cdot 4 \cdot 7 = 84 \, \text{m}^3 \]

Final Answer

The volume of the right circular cylinder is \(\boxed{84 \, \text{m}^3}\).

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