- #1

songoku

- 2,328

- 336

- Homework Statement
- Calculate the volume of solid having triangle base with vertices (0, 0) , (2, 0) and (0, 3) whose slice perpendicular to x-axis is semicircle

- Relevant Equations
- Volume = ##\int_p^{q} A(x) dx##

First, I tried to find the equation of line passing through (2, 0) and (0, 3) and I got ##y=3-\frac{3}{2}x##

Then I set up equation for the area of one slice, ##A(x)##

$$A(x)=\frac{1}{2} \pi r^2$$

$$=\frac{1}{2} \pi \left( \frac{1}{2}y\right)^2$$

$$=\frac{1}{2} \pi \left(\frac{3}{2}-\frac{3}{4}x \right)^2$$

Am I correct until this point? Thanks

Then I set up equation for the area of one slice, ##A(x)##

$$A(x)=\frac{1}{2} \pi r^2$$

$$=\frac{1}{2} \pi \left( \frac{1}{2}y\right)^2$$

$$=\frac{1}{2} \pi \left(\frac{3}{2}-\frac{3}{4}x \right)^2$$

Am I correct until this point? Thanks