The diameter of a conical paper cup is 3.4 inches, and the length of the sloping side is 4.53 inches, as shown in the figure. How much water will the cup hold? (Round your answer to two decimal places.)

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Guest Apr 24, 2019

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*The diameter of a conical paper cup is 3.4 inches, and the length of the sloping side is 4.53 inches, as shown in the figure. How much water will the cup hold? (Round your answer to two decimal places.)*

Turn the paper cup upside down. This is just to make it easier for me.

Draw a line from the point of the cone down to the middle of the circular base.

In two dimensions, that line is one side of a right triangle whose base is 1**.**7 inches and hypotenuse is 4**.**53 inches

Use Pythagoras' Theorem to determine the third side. This will be the height of the cone.

4**.**53^{2} = h^{2} + 1**.**7^{2}

rearrange terms for my convenience h^{2} = 4**.**53^{2} – 1**.**7^{2}

do the arithmetic h^{2} = 20**.**52 – 2**.**89 = 17**.**63

h = sqrt(17**.**63) = 4**.**20

you have the radius of the cone

and its height; use the formula V = (1/3) * pi * r^{2} * h

plug in the values V = (1/3) * 3**.**14 * 2**.**89 * 4**.**20

do the arithmetic V = 12**.**70 inch^{3}

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Guest Apr 24, 2019