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 yaxis, 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^2r^2) dx
= π∫[0,a] (2x)^2  (x^2)^2 dx
= πa^3(4/3a^2/5)
so, we want πa^3(4/3a^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
 calculus  Sketch the region R bounded by the graphs of the equations and find ...
 calculus  sketch the region R bounded by the graphs of the equations, and find ...
 calculus  Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real ...
 MATH Please Help Please  Algebra 2 There is a graphs of the sequence f(n)=2n3 ...
 Math  sketch the region bounded by the graphs of f(y)=(y/Squareroot of(16y^2...
 CalculusSteve  Find the area of the region between the graphs of f(x)=3x+8 and...
 maths  the region in the first quadrant bound by the graphs y=(x*x*x)/3 and y=...
 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 ...
More Related Questions