Geometry Geometry 3D Shapes & Solids 3 — Questions and Answers
Question 1: What is the surface area of a sphere with radius 4 cm?
- 16π cm²
- 32π cm²
- 48π cm²
- 64π cm² (Correct answer)
Correct answer: 64π cm²
Surface area of a sphere = 4πr² = 4π × 16 = 64π cm².
Question 2: The cross-section of a cylinder cut parallel to its base is a:
- Rectangle
- Ellipse
- Circle (Correct answer)
- Triangle
Correct answer: Circle
A horizontal cross-section of a cylinder parallel to its circular base is always a circle.
Question 3: A rectangular prism has length 5, width 3, and height 2. What is its surface area?
- 30
- 62 (Correct answer)
- 47
- 60
Correct answer: 62
SA = 2(lw + lh + wh) = 2(15 + 10 + 6) = 2(31) = 62.
Question 4: What is Euler's formula relating vertices (V), edges (E), and faces (F) of a polyhedron?
- V + E + F = 2
- V − E + F = 2 (Correct answer)
- V + E − F = 2
- V × E × F = 2
Correct answer: V − E + F = 2
Euler's formula states V − E + F = 2 for any convex polyhedron.
Question 5: A cone has a radius of 4 cm and a height of 3 cm. What is its slant height?
- 3 cm
- 4 cm
- 5 cm (Correct answer)
- 7 cm
Correct answer: 5 cm
Slant height l = √(r² + h²) = √(16 + 9) = √25 = 5 cm.
Question 6: How many faces does an octahedron have?
- 6
- 8 (Correct answer)
- 10
- 12
Correct answer: 8
A regular octahedron has 8 equilateral triangular faces.
Geometry Geometry 3D Shapes & Solids 3
What is the surface area of a sphere with radius 4 cm?