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GB-27-05-001 · Sphere and hemisphere

A solid hemisphere has radius 16.2 cm. Give answers to 1 decimal place. The volume of a sphere is 43πr3\frac43\pi r^3 and its surface area is 4πr24\pi r^2.

(a) Calculate the volume of the hemisphere.

(b) Calculate the total surface area, including the base.

Part (a) 3D Shapes: Hemisphere Volume & Surface Area Booklet p. 39
Method
1) Hemisphere volume = ½ × (4/3 πr³) = 2/3 πr³
2) Total surface area = curved (½ × 4πr² = 2πr²) + flat circular base (πr²) = 3πr²
Worked Example (GB-27-05-001 · Part (a))
Calculate the volume of the hemisphere.
1)
Halve the sphere volume.
2)
8904.4 cm³
Ans = 8904.4 cm³
Part (b) 3D Shapes: Hemisphere Volume & Surface Area Booklet p. 39
Method
1) Hemisphere volume = ½ × (4/3 πr³) = 2/3 πr³
2) Total surface area = curved (½ × 4πr² = 2πr²) + flat circular base (πr²) = 3πr²
Worked Example (GB-27-05-001 · Part (b))
Calculate the total surface area, including the base.
1)
Curved area 2πr² plus base area πr².
2)
2473.4 cm²
Ans = 2473.4 cm²