A cylindrical glass of water is 2.5 centimeters tall and holds a volume of 20 cubic centimeters of water. The radius of the glass is sqrt((p)/( pi)) centimeters, where p is a constant. What is the value of p ?

Volume Formula Substitution: The volume V of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder. We are given that the volume V is 20 cubic centimeters and the height h is 2.5 centimeters. We are also given that the radius r is sqrt(p/π) centimeters. We need to find the value of p.Simplify Equation: Substitute the given values into the volume formula: 20 = π(sqrt(p/π))^2 * 2.5. Simplify the equation by squaring the radius: 20 = π(p/π) * 2.5.Divide and Solve: Cancel out the π in the numerator and denominator: 20 = p * 2.5. Now we have a simple equation to solve for p.Calculate Value: Divide both sides of the equation by 2.5 to solve for p: p = 20 / 2.5.Calculate the value of p: p = 8. This is the value of the constant p.

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A cylindrical glass of water is 2.5 centimeters tall and holds a volume of 20 cubic centimeters of water.
The radius of the glass is
sqrt((p)/( pi)) centimeters, where
p is a constant. What is the value of
p ?

A cylindrical glass of water is $2$ . $5$ centimeters tall and holds a volume of $20$ cubic centimeters of water. $\newline$ The radius of the glass is $\sqrt{\frac{p}{\pi}}$ centimeters, where $p$ is a constant. What is the value of $p$ ?

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Q. A cylindrical glass of water is

2

5

centimeters tall and holds a volume of

20

cubic centimeters of water.

\newline

The radius of the glass is

\sqrt{\frac{p}{\pi}}

centimeters, where

p

is a constant. What is the value of

p

Given Information: The volume $V$ of a cylinder is given by the formula $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height of the cylinder. We are given that the volume $V$ is $20$ cubic centimeters and the height $h$ is $2.5$ centimeters. We are also given that the radius $r$ is $\sqrt{\frac{p}{\pi}}$ centimeters. We need to find the value of $p$ .
Volume Formula Substitution: Substitute the given values into the volume formula: $\newline$ $20 = \pi(\sqrt{\frac{p}{\pi}})^2 \times 2.5$ $\newline$ Simplify the equation by squaring the radius: $\newline$ $20 = \pi(\frac{p}{\pi}) \times 2.5$
Divide and Solve: Cancel out the $\pi$ in the numerator and denominator: $\newline$ $20 = p \times 2.5$ $\newline$ Now we have a simple equation to solve for $p$ .
Calculate Value of $p$ : Divide both sides of the equation by $2.5$ to solve for $p$ : $\newline$ $p = \frac{20}{2.5} = 8$ $\newline$ Therefore, the value of $p$ is $8$ .