Geometry Geometry 3D Shapes & Solids 2 — Questions and Answers
Question 1: The volume of a cylinder with radius 5 cm and height 10 cm is closest to:
- 157 cm³
- 314 cm³
- 785 cm³ (Correct answer)
- 1,570 cm³
Correct answer: 785 cm³
V = πr²h = π × 25 × 10 ≈ 785 cm³.
Question 2: How many vertices does a square pyramid have?
- 4
- 5 (Correct answer)
- 6
- 8
Correct answer: 5
A square pyramid has 4 base vertices plus 1 apex, totaling 5 vertices.
Question 3: What is the lateral surface area of a cone with radius 3 cm and slant height 7 cm?
- 21π cm² (Correct answer)
- 42π cm²
- 9π cm²
- 63π cm²
Correct answer: 21π cm²
Lateral surface area of a cone = πrl = π × 3 × 7 = 21π cm².
Question 4: A sphere has a radius of 6 cm. What is its volume?
- 72π cm³
- 144π cm³
- 288π cm³ (Correct answer)
- 432π cm³
Correct answer: 288π cm³
V = (4/3)πr³ = (4/3)π × 216 = 288π cm³.
Question 5: Which of the following describes a prism?
- Two parallel congruent polygonal bases connected by rectangles (Correct answer)
- One circular base and a curved surface meeting at a point
- All faces are equilateral triangles
- A perfectly round 3D shape with every point equidistant from center
Correct answer: Two parallel congruent polygonal bases connected by rectangles
A prism has two parallel congruent polygonal bases connected by rectangular lateral faces.
Question 6: How many faces does a pentagonal prism have?
- 5
- 6
- 7 (Correct answer)
- 10
Correct answer: 7
A pentagonal prism has 2 pentagonal bases + 5 rectangular lateral faces = 7 faces.
Geometry Geometry 3D Shapes & Solids 2
The volume of a cylinder with radius 5 cm and height 10 cm is closest to: