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I'm still confused on some of these volume problems, so please bear with me :)
Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of the cone is 10 ft.
Well, I'm not sure if a "nose cone" is a standard cone or is this like a frustrum?
I see a formula for 2pi*Int(0, 10) x*(1/4)x2dx but is that all there is to it?
Using the equation above I would get 2pi/4[(1/2)x^2*(x^3)/3] over interval 0 to 10
so: 2pi/4[50*1000/3]-0=2pi/4*50,000/3=100,000pi/12=25,000pi/3 This just seems way too huge.
Homework Statement
Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of the cone is 10 ft.
Homework Equations
Well, I'm not sure if a "nose cone" is a standard cone or is this like a frustrum?
I see a formula for 2pi*Int(0, 10) x*(1/4)x2dx but is that all there is to it?
The Attempt at a Solution
Using the equation above I would get 2pi/4[(1/2)x^2*(x^3)/3] over interval 0 to 10
so: 2pi/4[50*1000/3]-0=2pi/4*50,000/3=100,000pi/12=25,000pi/3 This just seems way too huge.