Question

The outline of a rugby ball has the shape of

x²/30+y²/16=1
The ball itself is the revolution of this ellipse about the x-axis. Find the volume of the ball.

Answer 1

To find the volume of the rugby ball, we need to find the volume of the solid generated by rotating an ellipse around the x-axis.

Step-by-step explanation:

The equation given represents the equation of an ellipse. To find the volume of the rugby ball, we need to find the volume of the solid generated by rotating the ellipse around the x-axis.

To find the volume of the solid generated by rotating the ellipse around the x-axis, we can use the formula for the volume of a solid of revolution:

V = π∫(R(x))^2dx

Where R(x) represents the radius of the cross-section of the solid at any given x-coordinate. In this case, the radius of the cross-section will be given by y = √(16 - 16x^2/30).

Substituting this value into the formula, we have:

V = π∫(√(16 - 16x^2/30))^2dx

Integrating this expression will give us the volume of the rugby ball.