A cylindrical juice glass is 8 centimeters tall and has a diameter of 6 centimeters. If the
glass is ¾ full, find the volume of the juice in the glass.
3/4 * 8 * 9π = 54π cm^3
108cm^3
To find the volume of the juice in the glass, we need to calculate the volume of the cylindrical glass and then multiply it by ¾.
The formula for the volume of a cylinder is:
V = π * r^2 * h
Where:
V is the volume of the cylinder
π is a mathematical constant approximately equal to 3.14159
r is the radius of the base of the cylinder
h is the height of the cylinder
Given that the glass has a diameter of 6 centimeters, we can find the radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 6 cm / 2 = 3 cm
The height (h) of the glass is given as 8 centimeters.
Now, we can substitute the values into the formula:
V = π * (3 cm)^2 * 8 cm
V = 3.14159 * 3^2 * 8
V = 3.14159 * 9 * 8
V = 226.19552 cm^3
Therefore, the volume of juice in the glass is 226.19552 cm^3.
To find the volume of the juice in the glass, we need to calculate the volume of the cylindrical part that is filled.
The formula for the volume of a cylinder is: V = πr²h, where V is the volume, r is the radius, and h is the height.
Here's how we can find the volume of the juice:
1. First, we need to calculate the radius of the cylindrical glass. The diameter is given as 6 centimeters, so we can find the radius by dividing the diameter by 2:
radius = diameter / 2 = 6 cm / 2 = 3 cm.
2. Next, we need to calculate the height of the juice filled in the glass. The glass is 8 centimeters tall, and it is 3/4 full. So, the height of the juice is:
juice_height = 8 cm * (3/4) = 6 cm.
3. Now we can plug in the values into the formula for the volume of the cylinder:
V = π * (radius)² * juice_height = π * 3² * 6 cm³ ≈ 169.65 cm³.
Therefore, the volume of the juice in the glass is approximately 169.65 cm³.