Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 5√49 − x2

y = 0

x = 2

x = 4

Answer 1

V = 4316.75 π

Explanation:

Given that:

`y = 5 √(49 -x^2)` y = 0, x = 2, x = 4

`V = \pi \int \limits ^(x=4)_(x=2) y^2 \ dx`

where;

y² = 25 (49 - x²)

`V = 25 \pi \int \limits ^4_2 (49-x^2) dx`

`V = 25 \pi [ (49x-(x^3)/(3)]^4_2`

`V = 25 \pi [ 49* 4 -(4^3)/(3) - 2]`

`V = 25 \pi [ 196-21.33 - 2]`

`V = 25 \pi [ 172.67]`

V = 4316.75 π