Case Study 1: Water Tank
A school installed a cylindrical water tank of radius 1.4 m and height 3.5 m. The tank was painted from outside and also used to store water.
Questions:
- Curved surface area = ?
(a) 20 m² (b) 22 m² (c) 30.8 m² (d) 30.8 m² × 10
Answer: (d) - Formula for curved surface area of cylinder = ?
(a) 2πrh (b) πr²h (c) 2πr² (d) none
Answer: (a) - Volume of tank = ?
(a) πr²h (b) 2πrh (c) 4/3 πr³ (d) none
Answer: (a) - Unit of volume = ?
(a) m² (b) m³ (c) cm (d) none
Answer: (b) - Unit of surface area = ?
(a) m² (b) m³ (c) cm³ (d) none
Answer: (a)
Case Study 2: Ice Cream Cone
An ice cream cone has a height of 9 cm and base radius of 3 cm, with a hemisphere of same radius on top.
Questions:
- Volume of cone = ?
(a) 1/3 πr²h (b) πr²h (c) 2πrh (d) none
Answer: (a) - Volume of hemisphere = ?
(a) 2/3 πr³ (b) 4/3 πr³ (c) πr²h (d) none
Answer: (a) - Total volume of ice cream = ?
(a) sum of cone + hemisphere (b) difference (c) product (d) none
Answer: (a) - Surface area includes?
(a) CSA of cone + CSA of hemisphere (b) TSA of cone only (c) TSA of hemisphere only (d) none
Answer: (a) - Combination solid is formed by = ?
(a) cone + hemisphere (b) cylinder + sphere (c) cuboid + cone (d) none
Answer: (a)
Case Study 3: Medicine Capsule
A medicine capsule is in shape of cylinder with two hemispheres at both ends. Radius is 0.7 cm, length is 2 cm.
Questions:
- Shape = ?
(a) sphere (b) cylinder + 2 hemispheres (c) cuboid (d) cone
Answer: (b) - Volume = ?
(a) πr²h + 4/3 πr³ (b) πr²h + 2/3 πr³ (c) 2πrh (d) none
Answer: (a) - Surface area = ?
(a) 2πrh + 4πr² (b) 2πrh + 2πr² (c) πr²h (d) none
Answer: (a) - Capsule is useful for?
(a) liquid (b) medicine (c) gases (d) none
Answer: (b) - Units of volume here = ?
(a) cm² (b) cm³ (c) m³ (d) none
Answer: (b)
Case Study 4: Spherical Balloon
A balloon is spherical with radius 7 cm.
Questions:
- Volume = ?
(a) 4/3 πr³ (b) πr²h (c) 2πrh (d) none
Answer: (a) - Surface area = ?
(a) 4πr² (b) 2πrh (c) 2πr² (d) none
Answer: (a) - Volume increases with?
(a) r³ (b) r² (c) r (d) none
Answer: (a) - Surface area increases with?
(a) r³ (b) r² (c) r (d) none
Answer: (b) - If radius doubles, volume increases by?
(a) 2 times (b) 4 times (c) 6 times (d) 8 times
Answer: (d)
Case Study 5: Storage Box
A cuboidal box measures 60 cm × 40 cm × 30 cm.
Questions:
- Volume = ?
(a) l × b × h (b) 2(lb+bh+hl) (c) 4/3 πr³ (d) none
Answer: (a) - TSA = ?
(a) 2(lb+bh+hl) (b) l × b × h (c) πr²h (d) none
Answer: (a) - LSA = ?
(a) perimeter of base × height (b) 2h(l+b) (c) both (d) none
Answer: (c) - Unit of surface area = ?
(a) cm² (b) cm³ (c) m³ (d) none
Answer: (a) - Unit of volume = ?
(a) cm² (b) cm³ (c) m² (d) none
Answer: (b)
Case Study 6: Cone Decoration
A tent is in the shape of cone with radius 7 m, height 24 m.
Questions:
- Slant height = ?
(a) 24 (b) 25 (c) 26 (d) none
Answer: (b) - CSA = ?
(a) πrl (b) 2πrh (c) πr² (d) none
Answer: (a) - Volume = ?
(a) 1/3 πr²h (b) πr²h (c) 2πrh (d) none
Answer: (a) - Area of base = ?
(a) πr² (b) 2πrh (c) πrl (d) none
Answer: (a) - Formula for l = ?
(a) √(r²+h²) (b) r+h (c) r-h (d) none
Answer: (a)
Case Study 7: Hemisphere Bowl
A bowl is hemispherical, radius 7 cm.
Questions:
- Volume = ?
(a) 2/3 πr³ (b) 4/3 πr³ (c) πr²h (d) none
Answer: (a) - CSA = ?
(a) 2πr² (b) πr² (c) 4πr² (d) none
Answer: (a) - TSA = ?
(a) 3πr² (b) 2πr² (c) πr² (d) none
Answer: (a) - If r doubles, volume increases by?
(a) 2 times (b) 4 times (c) 8 times (d) none
Answer: (c) - Bowl is shape of?
(a) hemisphere (b) cone (c) cuboid (d) none
Answer: (a)
Case Study 8: Cylindrical Pipe
A hollow cylindrical pipe has outer radius 14 cm, inner radius 7 cm, height 20 cm.
Questions:
- Volume = ?
(a) πh(R²−r²) (b) 2πrh (c) πr²h (d) none
Answer: (a) - Surface area includes?
(a) CSA inner + CSA outer + 2 rings (b) only outer CSA (c) only inner CSA (d) none
Answer: (a) - Shape of cross-section = ?
(a) annulus (ring) (b) circle (c) square (d) none
Answer: (a) - Pipe used for?
(a) water flow (b) decoration (c) storage (d) none
Answer: (a) - Formula for volume of hollow cylinder = ?
(a) πh(R²−r²) (b) 2πrh (c) πr²h (d) none
Answer: (a)
Case Study 9: Candle
A candle is made of a cylinder of height 10 cm and radius 3.5 cm, with a conical top of height 7 cm.
Questions:
- Volume = ?
(a) πr²h(cylinder) + 1/3 πr²h(cone) (b) only cylinder (c) only cone (d) none
Answer: (a) - Shape = ?
(a) cylinder + cone (b) sphere (c) cuboid (d) none
Answer: (a) - Surface area includes?
(a) CSA of cylinder + CSA of cone + base (b) only CSA cylinder (c) only cone (d) none
Answer: (a) - Formula for cone volume = ?
(a) 1/3 πr²h (b) πr²h (c) 2πrh (d) none
Answer: (a) - This is an example of?
(a) combination of solids (b) single solid (c) polygon (d) none
Answer: (a)
Case Study 10: Dome Building
A dome of temple is hemispherical with radius 14 m, placed on a cylindrical base of radius 14 m and height 6 m.
Questions:
- Shape formed = ?
(a) hemisphere + cylinder (b) cone + hemisphere (c) cuboid (d) none
Answer: (a) - Total height = ?
(a) 14 (b) 20 (c) 6 (d) 28
Answer: (b) - Volume = ?
(a) πr²h + 2/3 πr³ (b) πr²h + 4/3 πr³ (c) 2πrh (d) none
Answer: (a) - Surface area = ?
(a) CSA of cylinder + CSA of hemisphere + base (b) only hemisphere (c) only cylinder (d) none
Answer: (a) - Formula for CSA of hemisphere = ?
(a) 2πr² (b) 3πr² (c) 4πr² (d) none
Answer: (a)