Practice Square vs Cube Intuition in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Understanding x2 as the area of a square with side x (2D), and x3 as the volume of a cube (3D).

52=25 is a 5×5 square's area. 53=125 is a 5×5×5 cube's volume.

Showing a random 20 of 50 problems.

Example 1

easy
A square has side 1. What is its area?

Example 2

easy
Compute 23.

Example 3

medium
A square's side triples from 2 to 6. By what factor does its area change?

Example 4

hard
A square has area x and a cube has volume x, both with the same number x. The square's side equals the cube's edge. Find all positive x.

Example 5

medium
A storage box is a cube with edge 0.5 m. How many cubic centimetres of stuff does it hold?

Example 6

easy
Which is larger, 42 or 43?

Example 7

easy
Compute 62 and state what shape it represents.

Example 8

easy
A square has side length 4. What is its area?

Example 9

challenge
Two cubes have edges a and 2a. Show by what factor the larger cube's volume exceeds the smaller, for any a.

Example 10

easy
A square's area is 36. What is its side length?

Example 11

easy
A cube has volume 216 cm³. Find its edge.

Example 12

challenge
A cube and a square share the same numeric measure: a cube of edge x has volume equal to the area of a square of side x. Find all positive x.

Example 13

easy
A cube has edge 4 cm. Find its volume.

Example 14

easy
A square has side 7. Find its area.

Example 15

hard
A cube has total surface area 150 cm². Find its volume.

Example 16

challenge
A cube of edge a and a cube of edge b have a combined volume equal to a single cube of edge c. If a=3,b=4, find c (to 3 decimal places).

Example 17

easy
Compute 33 and state what shape it represents.

Example 18

medium
Which is larger: the area of a square of side 10, or the volume of a cube of edge 4?

Example 19

medium
A square tile has area 49 and a cube has volume 64. Which has the larger side/edge length?

Example 20

medium
A square's side length doubles from 3 to 6. By what factor does its area change?
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