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Questions and Answers
What is the formula for the surface area of a hemisphere?
What is the formula for the surface area of a hemisphere?
- $S = 2πr^2$
- $S = 4πr^3$
- $S = πr$
- $S = 4πr^2$ (correct)
What is the volume of a hemisphere if its radius is 8 cm?
What is the volume of a hemisphere if its radius is 8 cm?
- $V = 256π$ cm³
- $V = 512π$ cm³ (correct)
- $V = 682.67π$ cm³
- $V = 1024π$ cm³
What is the surface area of a sphere with radius 10 cm?
What is the surface area of a sphere with radius 10 cm?
- $S = 400π$ cm² (correct)
- $S = 300π$ cm²
- $S = 100π$ cm²
- $S = 200π$ cm²
A hollow sphere has an inner radius of 7 cm and an outer radius of 9 cm. What is its surface area?
A hollow sphere has an inner radius of 7 cm and an outer radius of 9 cm. What is its surface area?
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A hollow sphere has an inner radius of 5 cm and an outer radius of 8 cm. What is its volume?
A hollow sphere has an inner radius of 5 cm and an outer radius of 8 cm. What is its volume?
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Study Notes
Hemisphere Formulas
- The formula for the surface area of a hemisphere is 3πr², where r is the radius of the hemisphere.
- The formula for the volume of a hemisphere is (2/3)πr³, where r is the radius of the hemisphere.
Hemisphere Problems
- If the radius of a hemisphere is 8 cm, its volume is (2/3)π(8)³ = (2/3)π(512) = (1024/3)π ≈ 1074.91 cm³.
Sphere Formulas
- The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere.
Sphere Problems
- If the radius of a sphere is 10 cm, its surface area is 4π(10)² = 400π ≈ 1256.64 cm².
Hollow Sphere Formulas
- The formula for the surface area of a hollow sphere is 4πr₁² + 4πr₂², where r₁ is the inner radius and r₂ is the outer radius of the hollow sphere.
- The formula for the volume of a hollow sphere is (4/3)π(r₂³ - r₁³), where r₁ is the inner radius and r₂ is the outer radius of the hollow sphere.
Hollow Sphere Problems
- If the inner radius of a hollow sphere is 7 cm and the outer radius is 9 cm, its surface area is 4π(7)² + 4π(9)² = 196π + 324π = 520π ≈ 1632.62 cm².
- If the inner radius of a hollow sphere is 5 cm and the outer radius is 8 cm, its volume is (4/3)π((8)³ - (5)³) = (4/3)π(512 - 125) = (387/3)π ≈ 404.78π ≈ 1274.91 cm³.
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