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 Pi. Round to the nearest hundredth. Recall the formulas V = B h and V = four-thirds pi r cubed 226.08 cubic millimeters 310.86 cubic millimeters 339.12 cubic millimeters 1,808.64 cubic millimeters

Answer 1

The volume of new medicine capsule is 339.12 cubic millimeters

Explanation:

EDG 2020

Answer 2

The volume of new medicine capsule is 339.12 cubic millimeters, if the cylinder portion of the capsule is 8 millimeters long and has a diameter of 6 millimeters.

Explanation:

The given is,

Capsule shaped like a cylinder with a half sphere at each end

The cylinder portion of the capsule is 8 millimeters long

A diameter of 6 millimeters

`\pi` = 3.14

Step:1

Volume of new medicine capsule = Volume of cylinder +

2( Volume of half sphere ).....(1)

Step:2

Formula for Volume of cylinder,

`V_(cylinder) = Bh`......................(2)

Where, B - Base area of cylinder

h - Height of cylinder

Base area,
`B=\pi r^(2)`

Radius of cylinder, r = 3 millimeters (
`r= (d)/(2) = (6)/(2) = 3` )

B =
`\pi` ×
`3^(2)`

= 3.14 × 9

B = 28.26 square millimeters

Equation (2) becomes,

`V_(cylinder)` = ( 28.26 × 8 )

= 226.08

`V_(cylinder)` = 226.08 cubic millimeters

Step:3

Formula for volume of half sphere,

`V_(Half sphere) = (2)/(3) \pi r^(3)`..........................(3)

Where, r - Radius of sphere

From given, r = 3 millimeters (
`r= (d)/(2) = (6)/(2) = 3` )

Equation (3) becomes,

`V_(Half sphere) = (2)/(3) \pi 3^(3)`

= ( 0.666667 × 3.14 × 27 )

= 56.52 cubic millimeters

Capsule have half sphere at each end so the volume of half sphere is multiplied by 2.

= 2 × Volume of half sphere

= 2 × 56.52

= 113.04 cubic millimeters

Step:4

Volume of new medicine capsule = 226.08 + 113.04

= 339.12 cubic millimeters

Result:

The volume of new medicine capsule is 339.12 cubic millimeters, if the cylinder portion of the capsule is 8 millimeters long and has a diameter of 6 millimeters.