Question
Asked Dec 9, 2019
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Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve
x= 10y - 10y° and the y-axis about the given axes.
%3D
a. The x-axis
b. The line y = 1
a. The volume is
(Type an exact answer in terms of .)
b. The volume is
(Type an exact answer in terms of .)
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Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve x= 10y - 10y° and the y-axis about the given axes. %3D a. The x-axis b. The line y = 1 a. The volume is (Type an exact answer in terms of .) b. The volume is (Type an exact answer in terms of .)

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Expert Answer

Step 1

The given curves are , x = 0 and y = 1.

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2 y=1 (0, 1) x =10y -10y X =0 -5 10 -10 (0, –1)

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Step 2

a. Compute the volume of the shaded region of the solid a...

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V =2a[f (r)dv = 27[v(10y–10y )cy -2rj(t0y* - 10,")* = 27|(10y² – 10 y*)chv 10 y = 27 10y 3 5 10(1)' 10(1) = 27 3 5 50 – 30 4 = 27 = 27 15 87 3 87 Thus, the volume of the solid about x-axis is 3

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