Jasmine made a cylinder vase in which the sum of the lateral area and area of one base was about 3 thousand square cm. the vase had a height of 50cm. find the radius of the vase, explain the method you would use to find the radius?

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goformit100 · Answer

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anonymous · Answer

Well. I can't get it pretty but..
$$
\pi r^2 + 2\pi r \cdot 50 = 3000 \
\pi r^2 + 100\pi r -3000 = 0 \
r_{1,2} = \frac{-100\pi \pm \sqrt{(-100\pi)^2 - 4 \cdot \pi \cdot (-3000)} }{2\pi} \
r_{1,2} = \frac{-100\pi \pm \sqrt{10000\pi^2 +12000\pi} }{2\pi} \
r_{1,2} = \frac{-314.15 \pm 369.32 }{2\pi} \
r_{1} = \frac{-314.15 + 369.32 }{2\pi} = \frac{55.16}{6.28} = 8.78 \
r_{2} = \frac{-314.15 - 369.32 }{2\pi} = -\frac{683.47}{2\pi}\
$$
Since we know a radius can't be negative we are left with 8.78cm
$$
\pi \cdot 8.78^2 + 100 \pi \cdot 8.78 = 
242.18 + 2758.31 = 3000.49
$$
Since I rounded we get a very close result