What is the volume, in cubic length units, formed by revolving around the x-axis the area bounded by the curve y= (12.25 - x^2 )^1/2 and the-x axis.
The text book gives the following answers....My teacher said it is one of the numerical answers given.
a. 9pi/2
b. 32pi/3
c. 125pi/6
d. 36pi
e. 343pi/6
f. 256pi/3
g. 243pi/2
h. 500pi/3
i. none of these
2006-12-03 02:36:31 · 7 answers · asked by chris 2 in Science & Mathematics ➔ Mathematics
The answer is e.
2006-12-03 02:40:27 · answer #1 · answered by Anonymous · 1⤊ 1⤋
I won't do the math, but I will give you a good approach.
The area under the curve is the integral of f(x). The volume is the rotated area, so, since volume of a cylinder is pi*r^2, and r is f(x), you get
pi times f(x)^2 times the integral of f(x).
It has been a while!
2006-12-03 02:44:33 · answer #2 · answered by maddojo 6 · 1⤊ 0⤋
If you happen to notice that....
y = √(12.25 - x²) so
y² = 12.25 - x²
x² + y² = 12.25
So it's a circle! with radius 3.5.
Since you're rotating around the x-axis, you should get a sphere.
The volume of a sphere is 4/3πr³.
4/3π(3.5)³ = 42.875(4)/3π = 171.5π/3 = 343π/6
So it's e.
------------------------------------------------------------------------
Disk/Cross-Section Method:
The area of a cross section would be the area of a circle with the function as the radius:
A(x) = π(√(12.25 - x²))² = π(12.25 - x²)
And the function crosses the x-axis at:
0 = (12.25 - x²)
x = ±3.5
So the volume is:
3.5
⌠
⌡ π(12.25 - x²) dx
-3.5
π(12.25x - 1/3x³) from -3.5 to 3.5
π(12.25(3.5) - 1/3(3.5)³ - 12.25(-3.5) + 1/3(-3.5)³)
π(42.875 - 42.875/3 + 42.875 - 42.875/3)
π/3(128.625 - 42.875 + 128.625 - 42.875)
π/3(171.5)
343π/6
2006-12-03 02:59:40 · answer #3 · answered by Jim Burnell 6 · 2⤊ 0⤋
2X +8= X**2 -6 => 0= X**2 -2X -14 => (that's of the style aX**2 +bX +c= 0) a=a million, b= (-2), c= (-14) the roots are [-b+ SQRT(b**2-4ac]/ 2a and [-b- SQRT(b**2-4ac)]/2a root a million= [-(-2)+ SQRT(4-- fifty six)]/ 2(a million)= [2+SQRT (60)]/2=a million+SQRT(15) root 2= a million- SQRT(15)
2016-12-10 21:00:48 · answer #4 · answered by ? 4 · 0⤊ 0⤋
wow, I'm stumped! that's a good one, dang, what a bad time for albert einstien to be dead
2006-12-03 02:55:03 · answer #5 · answered by Anonymous · 0⤊ 0⤋
I think it is E, but what do I know, I'm only in Pre - Algebra.
2006-12-03 02:50:26 · answer #6 · answered by Anonymous 3 · 1⤊ 0⤋
Yes, I figured it out.
2006-12-03 02:38:48 · answer #7 · answered by Rather be dead than red... 6 · 0⤊ 2⤋