Question

A juice seller was serving juice in a glass with a cylinder and hemispherical depression at its base. The height of the glass is 10 cm, and the diameter is 5 cm. Find the apparent and actual capacity. Use pi as 3.14.

A. Apparent capacity: 245 cm³, Actual capacity: 195 cm³
B. Apparent capacity: 195 cm³, Actual capacity: 245 cm³
C. Apparent capacity: 250 cm³, Actual capacity: 200 cm³
D. Apparent capacity: 200 cm³, Actual capacity: 250 cm³

Answer 1

The correct answer is option B. Apparent capacity: 195 cm³, Actual capacity: 245 cm³.

Step-by-step explanation:

In order to find the apparent and actual capacity of the glass, we first need to calculate the volume of the cylinder and the hemispherical depression separately.

The volume of the cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height. Given that the diameter is 5 cm, the radius (r) would be half of that, which is 2.5 cm. Substituting the values into the formula, we get V = 3.14 * (2.5 cm)² * 10 cm = 196.25 cm³.

The volume of the hemispherical depression can be calculated using the formula V = (2/3) * πr³, where r is the radius. Again, the radius (r) would be 2.5 cm. Substituting the values into the formula, we get V = (2/3) * 3.14 * (2.5 cm)³ = 65.417 cm³.

To find the apparent capacity, we add the volume of the cylinder and the hemispherical depression: 196.25 cm³ + 65.417 cm³ = 261.667 cm³.

The actual capacity would be the volume of the cylinder without the hemispherical depression: 196.25 cm³.

Therefore, the correct answer is option B. Apparent capacity: 195 cm³, Actual capacity: 245 cm³.