Answer:
Explanation:
To solve this problem, we can use the following formulae for the volume of a cylinder and a hemisphere:
Volume of a cylinder = πr²h
Volume of a hemisphere = 2/3πr³/2
where r is the radius of the cylinder or hemisphere, and h is the height of the cylinder.
(a) To find the length of the cylinder, we can subtract the combined length of the two hemispheres from the total length of the capsule:
Length of cylinder = Total length of capsule - 2 × radius of hemisphere
Length of cylinder = 20 mm - 2 × 3 mm (radius of hemisphere)
Length of cylinder = 14 mm
(b) To find the volume of the cylinder, we need to know the radius and height. Since the width of the capsule is given as 6 mm, and we know that the cylinder runs the full length of the capsule, we can use the following formula to find the radius of the cylinder:
Width = 2 × radius of hemisphere + diameter of cylinder
6 mm = 2 × 3 mm + diameter of cylinder
Diameter of cylinder = 6 mm
Radius of cylinder = 3 mm
Now we can use the formula for the volume of a cylinder to find the volume of the cylinder:
Volume of cylinder = πr²h
Volume of cylinder = π(3 mm)² × 14 mm
Volume of cylinder ≈ 395.8 mm³ (to 3 significant figures)
(c) The radius of each hemisphere is 3 mm (since they have the same radius as the cylinder), so we can use the formula for the volume of a hemisphere to find the volume of each hemisphere:
Volume of hemisphere = 2/3πr³/2
Volume of hemisphere = 2/3π(3 mm)³/2
Volume of hemisphere ≈ 56.55 mm³ (to 3 significant figures)
(d) To find the total volume of the capsule, we can add the volumes of the cylinder and the two hemispheres:
Total volume of capsule = Volume of cylinder + 2 × Volume of hemisphere
Total volume of capsule ≈ 509.9 mm³ (to 3 significant figures)
Therefore, the length of the cylinder is 14 mm, the volume of the cylinder is approximately 395.8 mm³, the volume of each hemisphere is approximately 56.55 mm³, and the total volume of the capsule is approximately 509.9 mm³.