Question

Problem 3a

Answer 1

Given information

Given that is a solid with known cross-sectional areas.

Step-by-step explanation

Step 1.

Let be the area of the cross-section of  in the plane perpendicular to the and passing through the point , where .

Here,  is a continuous function of  in the interval .

Let the planes divide into slabs each of width and .

Then area of each slab is   .

 

Add the volumes of each slab to get the approximate volume of  .