Mathematics, 08.04.2020 21:14 ecletcicbeauty946

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

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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.

Step-by-step 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 ( $r= \frac{d}{2} = \frac{6}{2} = 3$ )

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,

$V_{Half sphere} = \frac{2}{3} \pi r^{3}$ ..........................(3)

Where, r - Radius of sphere

From given, r = 3 millimeters ( $r= \frac{d}{2} = \frac{6}{2} = 3$ )

Equation (3) becomes,

$V_{Half sphere} = \frac{2}{3} \pi 3^{3}$

= ( 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.

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