Mathematics, 10.06.2020 17:57 allieb12334
At Robin's Snow Cones, the shaved ice portion of the cone is shaped like a perfect sphere with a diameter of 8 cm. Exactly half of the shaved ice sphere extends above the paper cup holder. What is the volume of ice that extends above the cup to the nearest cubic centimeter?
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Mathematics, 20.06.2019 18:04
Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?
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At Robin's Snow Cones, the shaved ice portion of the cone is shaped like a perfect sphere with a dia...
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