Question

If the quarter circle intersects the x-axis at the coordinate (- 3, 0) and is rotated around the y-axis what is the resulting 3 - D figure and determine its volume to the nearest cubic unit.

Answer 1

Volume of the hemisphere will be 57 cubic units.

Explanation:

A quarter circle which intersects the x-axis at (-3, 0) when rotated around the y-axis, 3-D figure formed will be a hemisphere.

As shown in the figure attached,

Radius of the hemisphere formed = 3 units

Volume of the hemisphere =
`(1)/(2)((4)/(3))\pi (r)^(3)`

=
`((2)/(3))\pi (r)^(3)`

=
`(2)/(3)\pi (3)^(3)`

= 18π

= 56.55 cubic units

≈ 57 cubic units

Therefore, volume of the hemisphere will be 57 cubic units