Question

A pharmaticeutical company is making a new medicine capsule shaped like a cylinder with a half sphere at each end. The

cylinder portion of the capsule is 8 millimeters long and has a diameter of 6 millimeters.
What is the volume of the figure? Use 3.14 for
Round to the nearest hundredth.
Recall the formulas V-Bh and
226 08 cubic millimeters
310.86 cubic millimeters
339.12 cubic millimeters
1808 64 cubic millimeters

Answer 1

339.12 cubic millimeters

Explanation:

The picture of the question in the attached figure

we know that

The volume of the figure is equal to the volume of the two hemispheres (one sphere) plus the volume of the cylinder

so

step 1

Find the volume of the cylinder

The volume is given by

`V=Bh`

where

B is the area of the base of cylinder

h is the height of cylinder

we have

`B=\pi r^(2)`

we have

`h=8\ mm`

`r=6/2=3\ mm` ----> the radius is half the diameter

`B=(3.14)(3)^(2)`

`B=28.26\ mm^2`

substitute

`V=(28.26)(8)=226.08\ mm^3`

step 2

Find the volume of the sphere

The volume is given by

`V=(4)/(3)\pi r^(3)`

we have

`r=6/2=3\ mm` ----> the radius is half the diameter

substitute

`V=(4)/(3)(3.14)(3)^(3)=113.04\ mm^3`

step 3

Adds the volumes

`226.08+113.04=339.12\ mm^3`