The capsule describe consists of 2 hemispheres (same) and 1 cylinder. We need to sum up the volume of the cylinder and the 2 same hemispheres.
We are given the radius of the cylinder as 3 and the height as 6. The formula for volume of cylinder is \(V=\pi r^{2} h\). Plugging in 3 for r and 6 for h gives us,
\(V=\pi (3)^{2} (6)=54\pi\).
We are given the radius is 3 for the hemisphere. The formula for volume of a hemisphere is half of the volume of a sphere. The formula for hemisphere is shown below.
\(V=\frac{\frac{4}{3}\pi r^{3}} {2}\). Plugging in 3 for r gives us,
\(V=\frac{\frac{4}{3}\pi (3)^{3}} {2}\)
\(V=\frac{\frac{4}{3}\pi*27}{2} \\=\frac{36\pi}{2}\\=18\pi\)
Now, since we have 2 same hemispheres, we multiply this answer by 2 to get total volume of the 2 hemispheres.
\(18\pi * 2= 36\pi\).
- Total volume of the capsule:
\(54\pi + 36\pi = 90\pi\)
In decimal, taking 3.14 as \(\pi\), it is \(90*3.14=282.6\)
Rounding to the nearest whole number gives us 283 millimeters squared.
ANSWER: Volume = \(90\pi mm^{3}\) and \(283 mm^{3}\)
