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svarner2001
26.05.2021 •
Mathematics
Find the height of the cylinder given the surface area and one
other dimension:r = 5 in SA
659,4 in?
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Ответ:
C 16 inches
Step-by-step explanation:
a cylinder is 2 circles (1 on top, 1 at the bottom) and a round "mantle" connecting the two circles.
so, the surface area is the sum of the areas of both circles and the "mantle".
this "mantle" can be cut open and cut off the circles, and then be placed flat on the table. then it is simply a rectangle with the side lengths cylinder height (h) and circle circumference.
circle area : pi × r²
circle circumference : 2 × pi × r
rectangle area :
length × width = circle circumference × h
SA = 659.4 inches² = 2×(pi × r²) + (2×pi×r)×h =
= 2×pi×25 + 2×pi×5×h = 50×pi + 10×pi×h
=> 659.4 - 50×pi = 10×pi×h
=> (659.4 - 50×pi) / (10×pi) = h = 16 inches
Ответ: