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3 years ago

How many of these pitchers can a cylinder with height 9 inches and 2r fill? Explain how you know.

Mathematics

1 answer:

irakobra [83]3 years ago

3 0

Answer:

4 pitches

Step-by-step explanation:

if a cylinder with height 9 inches and radius r is filled with water, it can fill a certain pitcher. how many of these pitchers can a cylinder with height 9 inches and radius 2r fill? explain how you know.

Solution:

The volume of a cylinder is given by:

V = πr²h;

where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.

A cylinder with height 9 inches and radius r can fill a certain pitcher. Therefore the volume of the cylinder is:

V = πr²h = πr²(9) = 9πr²

V = volume of pitcher = volume of cylinder with radius r = 9πr²

For a cylinder with height 9 inches and radius 2r its volume is:

V2 = πr²h = π(2r)²(9) = 36πr²

Therefore, the number of pitchers a cylinder with height 9 inches and radius 2r can fill is:

number of pitches = 36πr² / 9πr² = 4

Therefore a cylinder with height 9 inches and radius 2r can fill 4 pitches.

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n200080 [17]

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Step-by-step explanation:

Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.

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Additional comment

You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.

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This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)

You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.

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