Compute-the-volume-of-a-solid-bounded-by-a-surface-with-equation-x-2-y-2-z-2-2-a-3-x-

Question Number 20162 by ajfour last updated on 23/Aug/17

C o m p u t e t h e v o l u m e o f a s o l i d

b o u n d e d b y a s u r f a c e w i t h e q u a t i o n

{(x^{2} + y^{2} + z^{2})}^{2} = a^{3} x .

Answered by ajfour last updated on 23/Aug/17

s u r f a c e i s s y m m e t r i c a l a b o u t

x a x i s a n d r a n g e s f r o m x = 0 t o

x = a .

L e t x^{2} + y^{2} = r^{2}, T h e n

x^{2} + r^{2} = a \sqrt{a} (\sqrt{x})

V o l u m e V = \int_{0}^{a} π r^{2} d x

= π \int_{0}^{a} [a \sqrt{a} (\sqrt{x}) - x^{2}] d x

= π [\frac{2 a \sqrt{a} (x \sqrt{x})}{3} - \frac{x^{3}}{3}] ∣_{0}^{a}

V = \frac{π}{3} a^{3} .

Facebook Tweet Pin