1. Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder. If the base of the shed is of dimensions7 m*15 m and the height of the cuboidalportion is 8 m, find the volume of the air the shed can hold. 2. The inner diameter of a cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical raised portion reducing the capacity of the glass. If the height of the glass is 10 cm, find the apparent and actual capacity of the glass.
Answers
Volume of cylinder=(15×7×8+1/2×22/7×7/2×7/2×15)m³=1128.75m³
Hence the machine occupied=300m³ & the total space occupied by the workers=20×0.08m³=1.6m³
Hence the volume of air=(1128.75)-(300+1.6)=827.15m³
Solution: Volume of Cuboid = lbh
→ 7 m × 15 m × 8 m
→ 840 m³
Let's focus now on half cylinder, 7 m is diameter and 15 m.
Volume of cylinder = πr²h
→ 22/7 × (7/2)² × 15 m³
→ 22/7 × 7/2 × 7/2 × 15 m³
→ 22 × 1/2 × 7/2 × 15 m³
→ 577.5 m³
But since cylindrical shed is half hence,
→ 577.5 m³/2 = 288.75 m³
Total Volume = 840 m³ + 288.75 m³
→ 1128.75 m³
Volume occupied = Volume of machinery + Volume of 20 workers
→ 300 m³ + 20(0.08)m³
→ 301.6 m³
Remaining volume of air = 1128.75 m³ - 301.6 m³
→ 827.15 m³
Answer: 827.15 m³
2. Apparent Volume of glass (illusion) = πr²h
→ 22/7 × (5/2)² × 10 cm³
→ 22/7 × 25/4 × 10 cm³
→ 11/7 × 25 × 5 cm³
→ 196.25 cm³
Real volume of glass = Volume of cylinder - Volume of hemisphere
→ 196.25 cm³ - (⅔ πr³)
→ 196.25 cm³ - (⅔ × 22/7 × 5³/2³)
→ 196.25 cm³ - 32.73 cm³
→ 163.52 cm³
Answer: 196.25 cm³; 163.52 cm³
