A tennis ball can in the shape of a right circular cylinder holds 3 tennis balls snugly. If the radius is 3.5cm, what % of the tennis ball can is occuppied by air?
Where do I start?
I will be happy to critique your thinking on this.
I used a visual and calcutated the height as 10.5cm. The radius would be half of the 3.5 to equal 1.75. I used the formul v=pie squared (x) height. I get 101.02 for the volume. I'm not sure what I am supposed to do next. Am I even approaching this the correct way?
To find the percentage of the tennis ball can occupied by air, we first need to find the volume of the tennis ball can and the volume of the three tennis balls it holds. Then we can find the difference between these volumes and calculate the percentage.
Let's start with finding the volume of the tennis ball can.
The volume of a right circular cylinder is given by the formula:
V_cylinder = π * r^2 * h
Where:
π is a mathematical constant approximately equal to 3.14159
r is the radius of the cylinder
h is the height of the cylinder
In this case, the radius of the tennis ball can is given as 3.5 cm. We need to find the height of the cylinder.
Given that the tennis balls fit snugly in the can, each tennis ball will have a diameter of 2 * radius = 2 * 3.5 cm = 7 cm.
Therefore, the height of the cylinder can be calculated as:
h = 3 * diameter of a tennis ball
h = 3 * 7 cm = 21 cm
Now, calculate the volume of the cylinder using the values of the radius and height:
V_cylinder = π * (3.5 cm)^2 * 21 cm
Calculate the volume of the three tennis balls:
V_3_tennis_balls = 3 * (4/3) * π * (3.5 cm)^3
Finally, subtract the volume of the tennis balls from the volume of the cylinder to find the volume of the air:
V_air = V_cylinder - V_3_tennis_balls
To find the percentage, divide the volume of the air by the volume of the cylinder and multiply by 100:
Percentage of air = (V_air / V_cylinder) * 100
Using these calculations, you can find the percentage of the tennis ball can occupied by air.
To find the percentage of the tennis ball can occupied by air, we first need to calculate the volume of the can and the volume of the tennis balls it can hold.
1. Start by calculating the volume of the right circular cylinder, which represents the can. The volume of a cylinder can be calculated using the formula:
Volume of a cylinder = π * radius^2 * height
In this case, the radius of the can is given as 3.5 cm, but we need to find the height. Since the can holds 3 tennis balls snugly, the height of the cylinder will be equal to the diameter of the tennis ball, or 2 times the radius of the tennis ball.
Radius of the tennis ball = 3.5 cm
Diameter of the tennis ball = 2 * radius = 2 * 3.5 cm = 7 cm
Height of the cylinder = Diameter of the tennis ball = 7 cm
Now, substitute the values into the formula to find the volume of the can.
2. Next, calculate the volume of one tennis ball using the formula for the volume of a sphere:
Volume of a sphere = (4/3) * π * radius^3
For this calculation, we will use the radius of the tennis ball given as 3.5 cm.
3. Multiply the volume of one tennis ball by 3 to find the total volume of 3 tennis balls that the can can hold.
4. Finally, calculate the percentage of the can's volume occupied by air by subtracting the volume of the tennis balls from the volume of the can, dividing by the volume of the can, and multiplying by 100.
Percentage of can occupied by air = [(Volume of the can - Volume of tennis balls) / Volume of the can] * 100
Follow these steps to find the percentage of the tennis ball can occupied by air.