Answer:
\(V_c=54\pi\ mm^{3}\)
\(V_s=36\pi\ mm^{3}\)
\(V=90\pi mm^3=283\ mm^{3}\)
Step-by-step explanation:
Given : A capsule consisting of a cylinder of radius 3 mm and height 6 mm with a hemisphere on each end of radius 3 mm.
To find : What is the volume of the item described?
Solution :
First we find the volume of the cylinder,
The volume of a cylinder is
\(V_c=\pi r^{2} h\)
where,
r is the radius of the cylinder = 3 mm
h is the height of the cylinder = 6 mm
substitute the values
\(V_c=\pi \times 3^{2}\times 6\\V_c=54\pi\ mm^{3}\)
Secondly we find the volume of the two hemisphere,
The volume of the sphere is
\(V_s=\frac{4}{3} \pi r^{3}\)
where,
r is the radius of the cylinder = 3 mm
substitute the values,
\(V_s=\frac{4}{3} \pi 3^{3}\\V_s=36\pi\ mm^{3}\)
Thirdly we find the volume of the capsule,
The volume of the capsule = The volume of a cylinder + The volume of the two hemisphere
\(V=54\pi\ mm^{3}+36\pi\ mm^{3}\\V=90\pi\ mm^{3}\)
\(V=90\times 3.14\ mm^{3}=283\ mm^{3}\)
Therefore, Option 2,3 and 6 are correct.
