Saturday

April 19, 2014

April 19, 2014

Posted by **nicko** on Sunday, January 23, 2011 at 10:00pm.

- calculus -
**Reiny**, Sunday, January 23, 2011 at 10:48pmI hope you made a sketch

the line x=1 and x=2 intersect with the curve at (1,2) and (2,9)

so first of all i will calculate a solid cyliner about the y-axis with a radius of 2 and a height of 9

= π(2^2)(9) = 36π

I will then hollow out a part with radius 1 and up to a height of 2

that is π(1^2)(2) = 2π

now I will hollow-out the curved part from a height of 2 to a height of 9 with a radius of

x = (y-1)^(1/3)

taking horizontal slices

Volume cut out

= π[integral] x^2 dy from 2 to 9

= π[integral] (y-1)^(2/3) dy

= π (5/3)(y-1)^(5/3 from 2 to 9

= π( (3/5)(8^(5/3)) - (3/5)(1^(5/3))

= π(93/5) = 18.6π

so final volume = 36π - 2π - 18.6π = 15.4π

check my arithmetic

**Related Questions**

Calculus (Solid of Revolution) - The region R is bounded by the x-axis, x = 1, x...

calculus - if the region enclosed by the y-axis, the line y=2 and the curve y=...

AP Calculus - Let R be the region bounded by the x-axis and the graph of y=6x-x^...

calculus - sketch the region R bounded by the graphs of the equations, and find ...

calculus - 2. Let R be the region of the first quadrant bounded by the x-axis ...

calculus - Let R be the region in the first quadrant bounded by the graphs of y=...

Calculus - Use the disk method to find the volume of the solid generated when ...

calculus - Sketch the region R bounded by the graphs of the equations and find ...

Calculus - 5. Find the volume of the solid generated by revolving the region ...

calculus - Find the volume of the solid obtained by rotating the region bounded ...