Denise poured milk into a glass shaped like a right circular cylinder with a radius of 2 inches. When she added chocolate syrup to the milk, the height of the liquid in the glass increased by 1/2 inch. What was the volume of the chocolate syrup that Denise added to the glass of milk?

V = π*r^2*h

Insert values and solve.

2pir

2pie*

To calculate the volume of the chocolate syrup that Denise added to the glass of milk, we need to find the change in volume after adding the chocolate syrup, which is equal to the volume of the chocolate syrup.

Given:
- The glass is shaped like a right circular cylinder with a radius of 2 inches.
- The height of the liquid increased by 1/2 inch.

To calculate the volume of a right circular cylinder, we use the formula:

V = π * r^2 * h

Where:
- V is the volume
- π is a constant approximately equal to 3.14
- r is the radius of the base of the cylinder
- h is the height of the cylinder

In this case, the original volume of the milk is given by:

V_milk = π * 2^2 * h_milk

And the final volume of the mixture (milk + chocolate syrup) is:

V_mixture = π * 2^2 * (h_milk + 1/2)

The volume of the chocolate syrup can be calculated by finding the difference between the final volume and the original volume:

V_chocolate_syrup = V_mixture - V_milk

Substituting the values into the formulas, we get:

V_chocolate_syrup = (π * 2^2 * (h_milk + 1/2)) - (π * 2^2 * h_milk)

Simplifying further:

V_chocolate_syrup = π * 2^2 * (h_milk + 1/2 - h_milk)

V_chocolate_syrup = π * 2^2 * (1/2)

V_chocolate_syrup = π * 4 * (1/2)

V_chocolate_syrup = π * 2

Finally, the volume of the chocolate syrup that Denise added to the glass of milk is approximately equal to 2π cubic inches.