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.
