Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid. Then find its volume in terms of pi.

Question

highschoolmom2010 · Answer

attachment

phi · Answer

Did you make any progress ?

highschoolmom2010 · Answer

it is a cone

phi · Answer

for Q33 around the y-axis.

Now you need the equation for the volume of a cone...

highschoolmom2010 · Answer

$$V=\frac{ 1 }{ 3 }\pi r^2h$$

phi · Answer

next, you need r and h for your cone.

highschoolmom2010 · Answer

h=3 r=4

phi · Answer

looks good.  This graph was trying to trick you by not labeling all the marks.

highschoolmom2010 · Answer

yes i noticed that

phi · Answer

last step is replace h and r with the numbers and simplify.  But do not change pi to a number (because they want the answer "in terms of pi" )

highschoolmom2010 · Answer

$$V=\frac{ 1 }{ 3}\pi 4^2(3)$$
$$V=\frac{ 1 }{ 3}\pi 16(3)$$
$$V=\frac{ 1 }{ 3 }\pi 48$$
$$V=16 \pi$$

phi · Answer

yes

phi · Answer

But I would not have multiplied 16*3 to get 48
it is easier to first divide 3 into 3
$$ V=\frac{ 1 }{ \cancel{3}}\pi 16(\cancel{3}) = 16\pi$$

highschoolmom2010 · Answer

$$V=\frac{ 1 }{3}\pi r^2h$$
$$V=\frac{ 1 }{ 3 }\pi 3^2(4)$$
$$V \frac{ 1 }{ 3 }\pi 9(4)$$
$$V=\frac{ 1 }{ 3 }(36)\pi$$
$$V=12 \pi$$

highschoolmom2010 · Answer

is that right for #35 ? and oh ok

phi · Answer

Q35 looks trickier.
I think the shape is a bit like a bowl
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