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Questions and Answers
What is the formula for the surface area of a hemisphere?
What is the volume of a hemisphere if its radius is 8 cm?
What is the surface area of a sphere with radius 10 cm?
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?
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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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Description
Test your understanding of spheres, hemispheres, and hollow spheres with this interactive quiz. Challenge yourself with questions about their volumes and surface areas. Get immediate feedback and improve your knowledge of these geometric shapes.
