Mathematics, 30.08.2019 06:00 karlaaag
Asphere with a diameter of 16mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. how high is the cylinder?
a. 16 mm
b. 8 mm
c. 18 mm
d. 14 mm
Answers: 1
![R_{sphere}= \frac{1}{2} *16=8[mm]\\ A_{sphere}=4 \pi R^{2}\\ A_{cylinder}=2 \pi R(R+h)\\\\ 4\pi R^{2}=2 \pi R(r+h)\\ \frac{4\pi R^{2}}{2 \pi R} =r+h\\ h= \frac{4\pi R^{2}}{2 \pi R}-R=2R-R=R\\ R=8[mm]](/tpl/images/0211/1191/45194.png)
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