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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 2.52.5 centimeters tall and holds a volume of 2020 cubic centimeters of water. The radius of the glass is pπ\sqrt{\frac{p}{\pi}} centimeters, where pp is a constant. \newlineWhat is the value of pp?\newline□\square

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Q. A cylindrical glass of water is 2.52.5 centimeters tall and holds a volume of 2020 cubic centimeters of water. The radius of the glass is pπ\sqrt{\frac{p}{\pi}} centimeters, where pp is a constant. \newlineWhat is the value of pp?\newline□\square
  1. Volume Formula Substitution: The volume of a cylinder is given by the formula V=πr2hV = \pi r^2 h, where VV is the volume, rr is the radius, and hh is the height of the cylinder. We are given that the volume VV is 2020 cubic centimeters, the height hh is 2.52.5 centimeters, and the radius rr is pπ\sqrt{\frac{p}{\pi}} centimeters. We need to substitute these values into the volume formula and solve for VV00.
  2. Equation Simplification: Substitute the given values into the volume formula: V=πr2hV = \pi r^2h.20=π(p/π)2×2.520 = \pi(\sqrt{p/\pi})^2 \times 2.5Simplify the equation by squaring the radius and multiplying by the height.20=π(p/π)×2.520 = \pi(p/\pi) \times 2.5
  3. Solving for p: Simplify the equation by canceling out π\pi in the numerator and the denominator.20=p×2.520 = p \times 2.5Now, solve for pp by dividing both sides of the equation by 2.52.5.p=202.5p = \frac{20}{2.5}p=8p = 8

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