A hemispherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain?
Answer: Volume = 23πr3 = 23 × 227 × 3.5 × 3.5 × 3.5 ≈ 89.8 cm3.
Step-by-step solution
Given: Hemispherical bowl, r = 3.5 cm
To find: Volume of water it holds
To find: Volume of water it holds
Idea: A hemisphere is half a sphere, so its volume is 12 × 43πr3 = 23πr3.
- Volume of water = volume of hemisphere = 23πr3.½ mark
- = 23 × 227 × 3.5 × 3.5 × 3.5 = 23 × 22 × 0.5 × 12.25 = 269.53.1 mark
- ≈ 89.8 cm3.½ mark
The bowl holds about 89.8 cm³ of water.
Check: Full sphere of radius 3.5: 43 × 227 × 42.875 ≈ 179.67 cm3; half is 89.83 ✓.
Answer to write in the exam
V = 23πr3
= 23 × 227 × 3.5 × 3.5 × 3.5
∴ V ≈ 89.8 cm3
Common mistakes that cost marks
- Using 43πr3 (the whole sphere).
- Squaring instead of cubing the radius.
How this can come in the exam
MCQ (1 mark)
The volume of a hemisphere of radius 21 cm is (π = 227)
- 19 404 cm3
- 38 808 cm3
- 2772 cm3
- 9702 cm3
Show answer
(A) 19 404 cm3
23 × 227 × 9261 = 19 404 cm3.
Try one yourself
A hemispherical bowl has radius 7 cm. How many litres of soup does it hold? (π = 227)
Show answer
23 × 227 × 343 = 21563 ≈ 718.67 cm3 ≈ 0.72 L.
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