MAT 302 Assignment Problem 7.2

MAT 302 Assignment Problem 7.2 | Borough of Manhattan Community College

7.2 Volume The Disk Method

Question 1

1 point) The volume of the solid obtained by rotating the region enclosed by

y=e5x+4,y=0,x=0,x=0.5y=e5x+4,y=0,x=0,x=0.5

about the x-axis can be computed using the method of disks or washers via an integral

Question 2

(1 point) The volume of the solid obtained by rotating the region enclosed by

x=0,y=1,x=y2x=0,y=1,x=y2

about the line y=1y=1 can be computed using the method of disks or washers via an integral

Question 3

(1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y=4x2,x=1,y=0,

Question 4

(1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y=x2−16x+63,y=0;

Question 5

(1 point)

Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y=tan3(x),y=tan3⁡(x), y=1y=1, and x=0x=0 about the line y=1?y=1?

Question 6

(1 point) Find the volume of the solid whose base is the region in the first quadrant bounded by y=x7y=x7, y=1y=1, and the yy-axis and whose cross-sections perpendicular to the xx axis are squares.

Ans 6

Question 7

(1 point)
Suppose you are given a solid whose base is the circle x2+y2=49x2+y2=49 and the cross sections perpendicular to the xx-axis are triangles whose height and base are equal.

Find the area of the vertical cross section AA at the level x=3x=3.

Find the volume VV of the solid

Question 8

(1 point) Find the volume generated by rotating the given region about the specified line.