Given the curve y=(9-3x)^1/2
Find the volume formed when the curve is rotated about the x-axis from x=0 to x=3....

Question

Given the curve y=(9-3x)^1/2
Find the volume formed when the curve is rotated about the x-axis from x=0 to x=3....

campbell_st · Answer

well $$V = \pi \int\limits_{a}^{b} y^2 dx$$

so you have $$V = \pi \int\limits_{0}^{3} ((9 - 3x)^{1/2})^2 dx$$

campbell_st · Answer

$$so you have V = \pi \int\limits_{0}^{3} 9 - 3x dx$$

rmrjr22 · Answer

Would this be the Shell Method?

campbell_st · Answer

well is very straight forward $$V = \pi [ 9x - 3/2x^2] $$

just evaluate it now f(3) - f(0)  might be 13.5 pi units cubed

rmrjr22 · Answer

I ended up getting 42.412 units

campbell_st · Answer

well 13.5 x 3.14 is about the 43 as I don't have a calculator with me

rmrjr22 · Answer

There was another part to it... Compare this to the volume of the circular cylinder formed by rotating the line y=3 over the same interval about the x-axis. What is the relationship between the 2 volumes?

campbell_st · Answer

well the cylinder is easy... the radius is 3... distance from y = 0 (x axis) to y = 3) height of the cylinder is 3 units... distance between x = 0 and x = 3

use $$V = \pi r^2 h$$

campbell_st · Answer

I think the cylinder is larger

campbell_st · Answer

actually the cylinder is double the size.. 

$$V _{cylinder} = 27 \pi  $$

$$V _{curve} = 13.5 \pi$$

rmrjr22 · Answer

$$(3.14)\int\limits_{0}^{3}(3x)^2dx $$ ?

rmrjr22 · Answer

No... Thats not it...