THREE 2 INCH DIAMETER TENNIS BALLS SNUGLY FIT IN A CYLINDRICAL CAN. THE BALLS TOUCH THE SIDE, TOP AND BOTTON OF THE PLASTIC CAN. HOW MUCH AIR IS IN THE CAN? ROUND DECIMAL ANSWERS TO THE NEAREST TENTH OF A CUBIC INCH. SHOW OR EXPLAIN HOW YOU GOT YOUR ANSWER.
First, do not use all capitals. It is harder to read and is equivalent to SHOUTING online.
Volume of cylinder 6" high and 2" in diameter minus volume of three balls, each with a 1" radius.
Cylinder volume = pi * r^2 * h
Sphere volume = 4/3 pi * r^3
You can do the calculations.
To find out how much air is in the can, we first need to calculate the volume of the three tennis balls and then subtract it from the volume of the can.
1. Calculate the volume of a tennis ball:
The diameter of the tennis ball is given as 2 inches, so we can determine the radius by dividing the diameter by 2:
radius = diameter/2 = 2/2 = 1 inch
The formula for the volume of a sphere is:
volume = (4/3) * π * radius^3
Using this formula, we can calculate the volume of the tennis ball:
volume of single tennis ball = (4/3) * π * (1 inch)^3
2. Calculate the total volume of three tennis balls:
Since we have three tennis balls, we multiply the volume of a single ball by 3:
total volume of three tennis balls = 3 * volume of single tennis ball
3. Calculate the volume of the cylindrical can:
The can is cylindrical, and the balls fit snugly inside, touching the sides, top, and bottom. This means that the diameter of the can is equal to the diameter of the tennis ball, which is 2 inches.
The formula for the volume of a cylindrical can is:
volume of cylinder = π * r^2 * h
In this case, we need to determine the height (h) of the can. Since the tennis balls touch the top and bottom of the can, the height would be equal to the diameter of the tennis ball, which is 2 inches.
volume of can = π * (1 inch)^2 * 2 inches
4. Calculate the air volume in the can:
The air volume in the can is the total volume of the can minus the total volume of the three tennis balls:
air volume in the can = volume of can - total volume of three balls
5. Round the result to the nearest tenth of a cubic inch:
Lastly, we round the air volume in the can to the nearest tenth of a cubic inch.
By following these steps and performing the necessary calculations, you can determine the amount of air in the can.