what is the volume of the item described?

a capsule consisting of a cylinder of radius 3 mm and height 6 mm with a hemisphere on each end of radius 3 mm.

select the exact answer in terms of π and the approximate answer rounded to the nearest whole number.

283 mm³

81 π mm³

90 π mm³

254 mm³

54 π mm³

170 mm³

The capsule describe consists of 2 hemispheres (same) and 1 cylinder. We need to sum up the volume of the cylinder and the 2 same hemispheres.

We are given the radius of the cylinder as 3 and the height as 6. The formula for volume of cylinder is . Plugging in 3 for r and 6 for h gives us,

.

We are given the radius is 3 for the hemisphere. The formula for volume of a hemisphere is half of the volume of a sphere. The formula for hemisphere is shown below.

. Plugging in 3 for r gives us,

Now, since we have 2 same hemispheres, we multiply this answer by 2 to get total volume of the 2 hemispheres.

.

In decimal, taking 3.14 as , it is

Rounding to the nearest whole number gives us 283 millimeters squared.

ANSWER: Volume = and