A company wants to determine the amount of a vitamin mix that can be enclosed in a capsule like the one shown. The capsule has a radius of 3millimeters (mm) and a length of 10 mm. How much vitamin mix is needed?

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shilpa85475 shilpa85475 · Answer 1 · 2020-02-18T11:33:28+01:00

226.285 mm³ vitamin mix is needed

Solution:

Radius of the capsule = 3 mm

Volume of the hemisphere = [tex]\frac{2}{3} \pi r^{3}[/tex]

[tex]$\begin{aligned}&=\frac{2}{3} \pi \times 3^{3}\\&=18 \pi\end{aligned}[/tex]

Volume of the hemisphere = 18π

Volume of the 2 hemisphere = 2 × 18π = 36π

Radius of the cylinder = 3 mm

Height of the cylinder = 10 – 3 – 3 = 4 mm

Volume of the cylinder = [tex]$\pi r^{2} h[/tex]

[tex]$\begin{aligned}&=\pi \times 3^{2} \times 4\\&=36 \pi\end{aligned}[/tex]

Volume of the cylinder = 36π

Volume of the capsule = volume of the 2 hemisphere + volume of the cylinder

= 36π + 36π

= 72π

[tex]$=72 \times \frac{22}{7}[/tex]

= 226.285 mm³

Volume of the capsule = 226.285 mm³

Hence 226.285 mm³ vitamin mix is needed.