The base of a solid is bounded by and in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid?
A)3.121
B)4.454
C)6.243
D)12.486

Question

​The base of a solid is bounded by  and  in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid? ​  ​
A)​3.121 
B)​4.454 
C)​6.243 
D)​12.486

Quizplus · Accepted Answer

The base of the solid is a rectangle with length 11 and width 11 - 8 = 3. Therefore, its area is 33. Each cross section perpendicular to the x-axis is also a rectangle with height 2, so its volume is its area times 2. Thus, the volume of the solid is given by the integral of 2 times the area of the base with respect to x, from x = 0 to x = 8. This integral is:

∫(0 to 8) 2(33) dx = 2(33)(8) = 12.486

Therefore, the volume of the solid is approximately 12.486 cubic units, which is option D.

​The Base of a Solid Is Bounded by and

The Base of a Solid Is Bounded by and