Question

The base of a solid in the xy-plane is the circle x2 + y2 = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid?

Answer 1

Answer:

The volume of the solid will be = 134.1 cubic units.

Step-by-step explanation:

The base of a solid has the equation of a circle x² + y² = 16 in the xy-plane. Cross-sections perpendicular to the y-axis of the solid are semicircles.

Therefore, the solid will be the shape of a hemisphere.

Now, the radius of the hemisphere will be 4 units.

{Since the base of the hemisphere is on the xy-plane and have equation

x² + y² = 4²}

Therefore, the volume of the solid will be = $\frac{2}{3}\pi r^{3} = (\frac{2}{3})\times (\frac{22}{7}) \times (4^{3}) = 134.1$ cubic units. (Answer)