Posted by **algebra** on Monday, December 31, 2012 at 3:20pm.

Sketch the graphs of f(x) = x^2 and g(x) = 2x. Find a number a between 0 and 2 so that when the region between the graphs of f and g for 0 <= x <= a is revolved about the y-axis, the volume of the solid produced is 7pia3/12 . Please show all work

- math -
**Steve**, Tuesday, January 1, 2013 at 12:04am
v = ∫[0,a] π(R^2-r^2) dx

= π∫[0,a] (2x)^2 - (x^2)^2 dx

= πa^3(4/3-a^2/5)

so, we want πa^3(4/3-a^2/5) = 7/12 π a^3

4/3 - a^2/5 = 7/12

80 - 12a^2 = 35

12a^2 = 55

a = √(55/12)

- math -
**Steve**, Tuesday, January 1, 2013 at 12:05am
oops: √45/12 = √(15/2)

## Answer This Question

## Related Questions

- MATH Please Help Please - Algebra 2 There is a graphs of the sequence f(n)=2n-3 ...
- Math - sketch the region bounded by the graphs of f(y)=(y/Squareroot of(16-y^2...
- Calculus-Steve - Find the area of the region between the graphs of f(x)=3x+8 and...
- calculus - Sketch the region bounded by the graphs of the algebraic functions & ...
- Calc - If, for all real number x, f(x) = g(x) + 5, then on any interval [a, b], ...
- math - The region between the graphs of y=x^2 and y=2x is rotated around the ...
- math - The region between the graphs of x=y2 and x=5y is rotated around the ...
- math - The region between the graphs of x=y2 and x=5y is rotated around the ...
- math - The region between the graphs of x=y2 and x=5y is rotated around the ...
- Calculus - Find the area of the region between the graphs of f(x)=3x+8 and g(x)=...

More Related Questions