Geometry Geometry 3D Shapes & Solids 3

Question 1

What is the surface area of a sphere with radius 4 cm?

Accepted Answer

64π cm²

Answer

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:

Accepted Answer

Circle

Answer

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?

Accepted Answer

62

Answer

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?

Accepted Answer

V − E + F = 2

Answer

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?

Accepted Answer

5 cm

Answer

Slant height l = √(r² + h²) = √(16 + 9) = √25 = 5 cm.

Geometry Practice Test