Triangle Question - Area of region?

Question

A triangular region is defined by (1,1) (2,2) and (5,2) - if this region was turned into a solid by revolving it around the y-axis, what would the volume be?

I'm sort of stuck here. Do I need to just find the area of that region then multiply it by pi? Or is there something more to it?

Answer 1

Step 1:

The points on the triangle region are and .

Determine the centroid of the triangle formulas are : and .

Substitute and in above formulas.

If and are the two points then the component form of vector is

If and are the two points then the component form of vector is

Consider .

Area .

Area.

Apply Pappus theorem: Volume .

Substitute , Area in above equation.

Volume.

Solution :

The triangle of the area , and volume .