Mathematics, 06.03.2021 23:20 Marcus2935

How can you use the formula for the volume of cylinder to remember the formula for the volume of a cone and the volume of a sphere?

How can you use the formula for the volume of cylinder to remember the formula for the volume of a

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Answer from: loveyeti106838

Choice A

The formula for the volume of a cone is 1/3 the volume of a cylinder. The volume of a sphere is 4/3 the volume of a cylinder, where the height of the cylinder is the same as the radius of the sphere

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Explanation:

As the first screenshot shows, the volume of a cone is 1/3 the volume of a sphere. The radius of each are the same. The height of each are the same as well.

The first screenshot also mentions "The volume of the half sphere is 2/3 the volume of the cylinder". The diagram shows the height of the cylinder (h) is equal to the radius of the half sphere. Based on this, the volume of a full sphere of radius r will be 4/3 times the volume of the cylinder with the same radius and height of 2r. You can think of having a spherical tennis ball inside a cylindrical can.

The first screenshot shows this when your teacher computed $2*\frac{2}{3}*\pi*r^2*r$ to get $\frac{4}{3}\pi*r^3$

Note how $\frac{4}{3}\pi*r^3 = \frac{4}{3}\left(\pi*r^2*r\right)$

The stuff in parenthesis represents the volume of a cylinder with radius r and height h = r. This is one way to see that

SphereVolume = (4/3)*(CylinderVolume)

where the height of the cylinder is as discussed above.

Answer from: Quest

answer set (b) 0.5, 3/4 80% is in order from least to greatest.

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form. typically, the best form in which to evaluate rational numbers is in decimals. in order to convert a percent to a decimal, you would divide the given percentage by 100. you can also accomplish the conversion by moving the decimal point over two places to the left. for example, the decimal value of 80% is 80/100, or 0.8. in order to convert a fraction to a decimal, you need to divide the numerator by the denominator. for example, 3/4 is 0.75. so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.

Answer from: Quest

The shelves will hold 270 books in total

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