Let's use the method of cylindrical shells.

The parameter for a cylinder will be `y` from `y=0` to `y=pi.`

The radius of a cylinder (the distance to the axis of rotation) is `4-y,`

the height of a cylinder is `sqrt(sin(y)).`

The volume is `2pi int_0^pi (4-y)sqrt(sin(y)) dy.`

I believe "calculator"...

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Let's use the method of cylindrical shells.

The parameter for a cylinder will be `y` from `y=0` to `y=pi.`

The radius of a cylinder (the distance to the axis of rotation) is `4-y,`

the height of a cylinder is `sqrt(sin(y)).`

The volume is `2pi int_0^pi (4-y)sqrt(sin(y)) dy.`

I believe "calculator" means "computer algebra system" here. WolframAlpha says the answer is **36.57476**.