Question

When 120 cm^3 of water is poured into a cylinder, it reaches a height of 8 cm. More water is poured into the cylinder until it reaches a height of 20 cm. How much water is in the cylinder now?

A) 300 cm^3
B) 720 cm^3
C) 600 cm^3
D) 480 cm^3.

Answer 1

By using the ratio of heights, we find that when water reaches a height of 20 cm in the cylinder, it contains 300 cm³ of water. The correct answer is A) 300 cm³.

Step-by-step explanation:

When 120 cm³ of water is initially in the cylinder, it reaches a height of 8 cm. The volume of a cylinder is found using the formula V = πr²h, where V is the volume, r is the radius, and h is the height. We can calculate the volume of the cylinder when the water reaches 20 cm by using the ratio of the heights and the known initial volume. Since the heights are proportional to the volume for the same diameter cylinder, we can set up a proportion where 120 cm³ is to 8 cm as V is to 20 cm.

We find that V = (120 cm³ / 8 cm) * 20 cm, which simplifies to V = 15 cm³/cm * 20 cm = 300 cm³. Therefore, when the cylinder is filled to a height of 20 cm, it contains 300 cm³ of water. The correct answer to the question is A) 300 cm³.