A tennis ball can in the shape of a cylinder holds three tennis balls snugly. If the radius of a tennis ball is 3.5 cm, what percentage of the tennis ball can is occupied by air?
volume tennis ball can= PIr^2*3r
volume of tennis balls=4/3 PI r^3
divide the second by the first.
2.3cm^3
.022508352%
To solve this problem, we first need to find the volume of the tennis ball can and the volume of three tennis balls. Then we can calculate the percentage of the can that is occupied by air.
1. Finding the volume of the tennis ball can:
- The tennis ball can is in the shape of a cylinder.
- The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
- Since the can is snugly holding three tennis balls, the height of the can is equal to the diameter of a tennis ball.
- The diameter of a tennis ball is twice the radius, so the height of the can is 2 * 3.5 cm = 7 cm.
- Now we can calculate the volume of the can using the formula: V_can = π * (r_can)^2 * h_can, where r_can is the radius and h_can is the height of the can.
2. Finding the volume of three tennis balls:
- The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
- We need to find the volume of one tennis ball and then multiply it by three to get the total volume of three tennis balls.
- Now we can calculate the volume of one tennis ball using this formula: V_ball = (4/3) * π * r_ball^3, where r_ball is the radius of a tennis ball.
3. Calculating the percentage of the can occupied by air:
- To find the volume of air in the can, subtract the total volume of three tennis balls from the volume of the can.
- Volume of air = V_can - (V_ball * 3)
- Calculate the percentage of the can that is occupied by air by dividing the volume of air by the volume of the can, and then multiplying by 100.
- Percentage of air in the can = (Volume of air / Volume of can) * 100.
Now you can substitute the values and calculate the answer.