Question

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 √p/π centimeters, where p is a constant. What is the value of p?

Answer 1

The value of the constant p is determined by rearranging the formula of the cylinder's volume to solve for p, giving us the result that p equals 8.

Step-by-step explanation:

To find the value of p in the expression for the radius of the cylinder √p/π, we use the formula for the volume of a cylinder, V = πr²h. Given the volume of water the glass holds, which is 20 cubic centimeters, and the height of the glass, which is 2.5 centimeters, we can set up the equation as follows:

20 = π(√p/π)²(2.5)

This simplifies to:

20 = π(p/π)(2.5)

Dividing both sides by π and 2.5 gives:

8/π = p/π

Multiplying both sides by π to solve for p yields:

p = 8

Hence, the value of p is 8.