Use the general slicing method to find the volume of the solid whose base is the triangle with vertices (0,0), (7,0), and (0,7) and whose cross sections perpendicular to the base and parallel to the y-axis are semicircles.
(need exact answer in terms of pi)

please explain. The answer I was getting was 49pi/8, but my homework says that is wrong.

Figure is attached below:

Step-by-step explanation:

Given Data:

triangle vertices= A,B,C=(0,0), (7,0), (0,7)

Required: Find Volume of the solid=V=?

For this type of question we need to use the following formula of slicing method

where a and b are limits which shows that solid extends from with the known cross section area    perpendicular to x-axis.

From the Figure.2 we can see that limits are from to and the red line is the diameter of the given semi circle.

We can see that if x increases then the diameter decreases along the hypotenuse thus diameter of the semi circle

Radius is half of the diameter, so Radius of semi circle

Here, Area is the area of the semi circle

so

Putting values, we get

Putting values in Eq(1), we get

expanding formula ()

Putting we get everything zero that's why only have expression for value of as:

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.