Question

Please help

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

Answer 1

90π mm³ and 283

Step-by-step explanation: i took the test

Answer 2

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.

• Volume of Cylinder:

We are given the radius of the cylinder as 3 and the height as 6. The formula for volume of cylinder is
`V=\pi r^(2) h`. Plugging in 3 for r and 6 for h gives us,

`V=\pi (3)^(2) (6)=54\pi`.

• Volume of Hemisphere(s):

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.

`V=\frac{(4)/(3)\pi r^(3)} {2}`. Plugging in 3 for r gives us,

`V=\frac{(4)/(3)\pi (3)^(3)} {2}`

`V=((4)/(3)\pi*27)/(2) \\=(36\pi)/(2)\\=18\pi`

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

`18\pi * 2= 36\pi`.

• Total volume of the capsule:

`54\pi + 36\pi  = 90\pi`

In decimal, taking 3.14 as
`\pi`, it is
`90*3.14=282.6`

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

ANSWER: Volume =
`90\pi mm^(3)` and
`283  mm^(3)`