A bosu® ball in the shape of a hemisphere (half of a sphere)
The diameter of the ball is 58 centimeters and is completely filled with air.
How much air does the ball contain, in cubic centimeters? Round your answer to the nearest centimeter. (Use 3.14 for π.)
diameter is the measure of the circular end/bottom so divide that by 2 to get your radius and use the volume formula of a sphere and multiply that by half.
I don't get it.
Volume of a sphere:
V = 1.3333 * pi * r^2
Find that volume. The divide it in half to find the volume of the hemisphere.
To find the volume of the hemisphere, we need to use the formula for the volume of a sphere, but divide it by 2 since we only have half of a sphere. The formula for the volume of a sphere is:
V = (4/3) * π * r^3
where V is the volume, π is a mathematical constant (approximately equal to 3.14), and r is the radius of the sphere.
In this case, the diameter of the ball is given as 58 centimeters. To find the radius, we divide the diameter by 2:
r = d/2 = 58/2 = 29 centimeters
Now we can plug in the radius into the formula and calculate the volume of the hemisphere:
V = (4/3) * 3.14 * (29)^3/2
Calculating this expression gives us:
V ≈ (4/3) * 3.14 * 29^3/2 ≈ 53701.5 cubic centimeters
Rounding the answer to the nearest centimeter, the ball contains approximately 53702 cubic centimeters of air.