Exploring Some Geometric Themes — Practice

Question 1

In the Sierpinski Carpet, how many small squares remain after step 3?

Accepted Answer

512

Question 2

How many faces, edges and vertices does a hexagonal prism have?

Accepted Answer

8 faces, 18 edges, 12 vertices

Question 3

A cylinder has base radius 7 cm and height 10 cm. What are the sidelengths of the rectangle in its net? (Take π = 22/7)

Accepted Answer

44 cm × 10 cm

Question 4

Which of the following shapes can NEVER be the projection of a cube?

Accepted Answer

A pentagon

Question 5

The perimeter of the Koch Snowflake at step 0 is 3 units. What is it at step 3?

Accepted Answer

64/9 units

Question 6

A cuboid measures 8 cm × 6 cm × 5 cm. Find its surface area, and describe how many rectangles of each size its net contains.

Accepted Answer

236 cm², with two rectangles each of 8 × 6, 8 × 5 and 6 × 5 cm

Question 7

The corners of an equilateral triangle of side 6 cm are cut off as far as the marks that divide each side into thirds. Name the shape that remains, give its side length, and find what fraction of the original area it covers.

Accepted Answer

A regular hexagon of side 2 cm covering 2/3 of the original area

Question 8

An ant at one corner of a room 8 m long, 6 m wide and 4 m high must crawl along the walls, floor or ceiling to reach the opposite corner. Find the length of the shortest such path, and explain why it is not 18 m.

Accepted Answer

√(8² + 10²) = √164 ≈ 12.81 m

Practice — Exploring Some Geometric Themes

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