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

Answer:

V = 4316.75 π

Step-by-step explanation:

Given that:

$y = 5 \sqrt{49 -x^2}$ y = 0, x = 2, x = 4

$V = \pi \int \limits ^{x=4}_{x=2} y^2 \ dx$

where;

y² = 25 (49 - x²)

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

$V = 25 \pi [ (49x-\dfrac{x^3}{3}]^4_2$

$V = 25 \pi [ 49\times 4 -\dfrac{4^3}{3} - 2]$

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

$V = 25 \pi [ 172.67]$

V = 4316.75 π