(a) The semicircles have a diameter equal to x, or y/5. So, each semicircle has an area of
πd^2/2 = π/2 (y/5)^2 = πy^2/50
Now add up all the thin discs and you get a volume of
∫[0,10] π/50 y^2 dy = 20π/3
(b) Now the sections have diameter equal to y = 5x, so their area is
π/2 (5x)^2 = 25π/2 x^2
and thus the volume is
∫[0,2] 25π/2 x^2 dx = 100π/3
The base of a solid is the region bounded by the lines y = 5x, y = 10, and x = 0. Answer the following.
a) Find the volume if the solid has cross sections perpendicular to the y-axis that are semicircles.
b) Find the volume if the solid has cross sections perpendicular to the x-axis that are semicircles.
I'm confused as to how to do this. Could you please help? Thanks!
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Thank you so much!
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