Question

The area under the graph y=square root of x from x=0 to x=3 is rotated around the x-axis to form a solid. What is the volume of the solid?

Answer 1

The volume is `9/2pi` cubic units.

Explanation:

Recall that the area of a solid rotated around the x-axis on `[a, b]` is given by

`V = pi int_a^b (f(x))^2dx`

Thus the volume is given by

`V = pi int_0^3 (sqrt(x))^2 dx`

`V= pi int_0^3 x dx`

`V = pi[1/2x^2]_0^3`

`V = 9/2pi` cubic units.

Hopefully this helps!