A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 3 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volume of the cylinder and toy. (Take π=3.14).
Answers
Answer:
Explanation:
Given :
- Height of the cone (h) = 3 cm
- Diameter of the base (d) = 4 cm
To Find :
- Volume of toy & The difference of the volume of the cylinder and toy.
Solution :
Firstly, we need to find radius of hemisphere.
• Radius = d/2
=> r = 4/2
=> r = 2 cm
According to the question,
• Volume of toy = ¹/3 × πr²h + ²/3 × πr³
=> V = ¹/3 × 3.14 × 2² × 3 + ²/3 × 3.14 × 2³
=> V = 1.046 × 4 × 3 + 2 × 1.046 × 8
=> V = 12.552 + 16.736
=> V = 29.288 cm³
Now, we need to find height of cylinder,
• Height of cylinder = Height of cone + Radius of hemisphere
=> h = 3 + 2
=> h = 5 cm
• Volume of cylinder circumscribing = πr²h
=> V = 3.14 × 2² × 5
=> V = 3.14 × 4 × 5
=> V = 3.14 × 20
=> V = 62.8 cm³
Now,
• Difference of volume = Volume of cylinder circumscribing - Volume of toy
=> D = 62.8 - 29.288
=> D = 33.512 cm³
Hence :
Volume of toy & The difference of the volume of the cylinder and toy is 29.288 cm³ & 33.512 cm³ respectively.