Answer:
60 pi cubic units.
Step-by-step explanation:
Given that a region bounded by
[tex]y = \sqrt{1+x} \\x = 0\\ x = 10[/tex]
is revolved around x axis.
To find the volume of generated solid
we know that when a curve is rotated form x=a to x=b around x axis
Volume V = [tex]\int_a^b \pi y^2 dx\\[/tex]
Substitute a=0 , b =10 and [tex]y^2 =1+x[/tex]
we have
Volume = [tex]\int_0^{10} \pi (1+x) dx\\= \pi (x+\frac{x^2}{2)} \\=\pi(10+50)\\= 60\pi[/tex]
Hence volume would be 60 pi cubic units.
