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Mindy is a sculptor. She has a cylinder of stone with a radius of $3 \text{ m}$ and a height of $2\text{ m}$ . She needs to carve out a sphere of radius $1\text{ m}$ from the cylinder. Mindy must cut away $\frac{v}{3}\pi \text{ cubic meters } (\text{m}^{3})$ of stone from the cylinder in order to be left with the sphere. What is the value of $v$ ?

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Solve quadratic equations: word problems

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Q. Mindy is a sculptor. She has a cylinder of stone with a radius of

3 \text{ m}

and a height of

2\text{ m}

. She needs to carve out a sphere of radius

1\text{ m}

from the cylinder. Mindy must cut away

\frac{v}{3}\pi \text{ cubic meters } (\text{m}^{3})

of stone from the cylinder in order to be left with the sphere. What is the value of

v

?

Calculate Sphere Volume: Calculate the volume of the sphere that Mindy needs to carve out. $\newline$ Volume of a sphere formula: $V = \frac{4}{3}\pi r^3$ $\newline$ $V = \frac{4}{3}\pi(1)^3$ $\newline$ $V = \frac{4}{3}\pi$ cubic meters
Identify Volume of Stone: Identify the volume of the sphere as the volume of stone Mindy must cut away. $v = \frac{4}{3}\pi$ cubic meters
Volume Equals Sphere: Since the volume of the sphere is the volume Mindy must cut away, $v$ is equal to the volume of the sphere. $\newline$ $v = \frac{4}{3}\pi$

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