Sunday

December 21, 2014

December 21, 2014

Posted by **Johnathon** on Thursday, November 10, 2011 at 12:09pm.

The base of S is a circular disk with radius 2r. Parallel cross-sections perpendicular to the base are squares.

- calculus -
**Steve**, Thursday, November 10, 2011 at 12:54pmI may have this wrong, but here's how I see it:

Draw a circle of radius 2r. That's the base. Draw a chord perpendicular to the x-axis at distance x from the center. At this point,

x^2 + y^2 = 4r^2

Now, erect a square of height 2y on the base. That is a cross-section of the solid. It has area 4y^2

The volume is thus Int(4y^2 dx)[0,2r]

But, y^2 = 4r^2 - x^2

v = 4*Int(4r^2 - x^2) dx)[0,2r]

= 4*(4r^2 x - 1/3 x^3)[0,2r]

= 4(8r^3 - 8r^3/3)

= 32(2/3 r^3)

= 64/3 r^3

**Answer this Question**

**Related Questions**

Math - Find the volume V of the described solid S. The base of S is a circular ...

CALCULUS - The base of S is a circular disk with radius 3r. Parallel cross-...

Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...

Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...

Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...

calculus - volume of solid whose base is a circle with radius a, and cross ...

College Calculus - Find the volume of the solid with given base and cross ...

Calculus - The base of a solid is the region enclosed by the graph of x^2 + 4y^2...

calculus - Find the volume V of the described solid S. The base of S is an ...

Calculus - Find the volume of the solid whose base is the region bounded by y=x^...