Find the volume of the described solid S
The base of S is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
Some help please
Find the volume of the described solid S
The base of S is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
Some help please
Given $\displaystyle 9x^2 + 4y^2 = 36$, you have
$\displaystyle 4y^2 = 36 - 9x^2$
$\displaystyle y^2 = \frac{36 - 9x^2}{4} = 9 - \frac{9x^2}{4}$
Now, the length of each triangle base is 2y.
So the area of each triangle is $\displaystyle \frac{1}{2}y\sqrt{2}\cdot y\sqrt{2} = y^2$, which is $\displaystyle 9 - \frac{9x^2}{4}$.
Can you do the rest?