ShapesProperties
- 1 curved face and 1 flat circular face.
- 1 curved edge and no corners.
- Its volume is half that of the sphere.
- Its curved surface is half the surface of the sphere.
Why the formulas work
Half a sphere has half the volume, (2/3)πr³, and half the curved surface, 2πr². But cutting the sphere creates a new flat face, a circle of area πr². A solid hemisphere therefore has a total surface of 2πr² + πr² = 3πr². A hollow bowl has only the curved part.
Worked example
Take a hemisphere with radius 7 cm.
- Volume. Volume = (2 ⁄ 3) πr3. Here: (2 ⁄ 3) × π × 7 × 7 × 7 = 718.38 cm³ (with π = 22/7: 718.67 cm³).
- Curved surface area. Curved surface area = 2πr2. Here: 2 × π × 7 × 7 = 307.88 cm² (with π = 22/7: 308 cm²).
- Total surface area. Total surface area = 3πr2. Here: 3 × π × 7 × 7 = 461.81 cm² (with π = 22/7: 462 cm²).
Finding a missing measurement
From the total surface area of a solid hemisphere, r = √(T ÷ 3π): 462 cm² gives r² = 49, so r = 7 cm, taking π = 22/7. From the volume, r³ = 3V ÷ 2π: 19,404 cm³ gives r³ = 9261, so r = 21 cm.
Mistakes to avoid
- Giving 2πr² when the question asks for the total surface of a solid hemisphere.
- Adding the flat face for an open bowl, where it does not exist.
Where you see it
A bowl, a dome on a building, half a coconut shell, half a lemon and an igloo are hemispheres.
Try these
Work each one out, then tap to check.
A hemisphere has radius 21 cm. Find its volume, curved surface area and total surface area. Take π = 22/7.
Volume = 19,404 cm³; Curved surface area = 2,772 cm²; Total surface area = 4,158 cm².
A hemisphere has radius 4.2 cm. Find its volume, curved surface area and total surface area. Take π = 22/7.
Volume = 155.23 cm³; Curved surface area = 110.88 cm²; Total surface area = 166.32 cm².