At Westside Middle School, 10 percent, or 140 students, participate in soccer. How many students are in the school? Check all th
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Answer:
Step-by-step explanation:
The Pythagorean theorem is a theorem that can be applied to the sides of a right triangle. Please note that a right angle refers to an angle with a measure of (90) degrees. A box around an angle shows that the angle is a right angle, or has a measure of (90) degrees. The Pythagorean theorem states the following,
Where (a) and (b) are the legs of the triangle, or the side adjacent to the right angle in the right triangle. (c) is the side opposite the right angle, or the hypotenuse of the triangle. One can apply this theorem to the smallest triangle in the diagram to find (y),
Substitute,
Simplify,
Inverse operations,
Take a factor from out of the square root. Remember that a number times itself under the radical is equal to the number. This can be simply stated as the following: (),
The volume of the sphere would be 334933.33 cm³.
When comparing the formulas for the volume of a sphere and the volume of a cylinder, we think about the height of the sphere. The radius of the sphere goes from the center to each outer edge; therefore the height of the sphere, running from top and bottom of the sphere, is 2 times the radius or 2r.
Formula for volume of a cylinder:
V = πr²h
Substituting 2r for h:
V = πr²(2r) = 2πr³
The formula for the volume of a sphere:
V = (4/3)πr³
Since 4/3 < 2, the sphere has a smaller volume. The ratio of the volume of the sphere to the volume of the cylinder is 4/3:2, which can be written as:
This means that the volume of the sphere is 2/3 the volume of the cylinder. We take the volume of the cylinder, 502400, and multiply it by 2/3:
334,933.33
When comparing the formulas for the volume of a sphere and the volume of a cylinder, we think about the height of the sphere. The radius of the sphere goes from the center to each outer edge; therefore the height of the sphere, running from top and bottom of the sphere, is 2 times the radius or 2r.
Formula for volume of a cylinder:
V = πr²h
Substituting 2r for h:
V = πr²(2r) = 2πr³
The formula for the volume of a sphere:
V = (4/3)πr³
Since 4/3 < 2, the sphere has a smaller volume. The ratio of the volume of the sphere to the volume of the cylinder is 4/3:2, which can be written as:
This means that the volume of the sphere is 2/3 the volume of the cylinder. We take the volume of the cylinder, 502400, and multiply it by 2/3:
334,933.33