Cube


Cube = Three-Dimensional Shape with Six Square Faces (with all right angles)

cube



Basics
s = Side
SA = Surface Area = area covering all surfaces of cube (measured in square units)
V = Volume = space occupied by cube (measured in cubic units)
Right Angle = 90°

All of the angles in a cube are right angles.
A cube is a special version of a right rectangular prism in which all faces are equal.

The math involving the geometric cube often requires the calculation of arithmetic squares, square roots, cubes, and cube roots.

square is the squaring command.

2nd square root is the square root command.
2nd activates square root above square .

power 3   is the cubing command.

2nd powering is the cube root command.

2nd activates root above power .


Formulas (NOT provided by Mathematics Formula Sheet)

SA = 6s²
s = SA÷6

V = s³
s = ³V


Question

The side of an ice cube is 2.5 centimeters.
What is its surface area?

Answer
37.5 square centimeters

Answer Process
SA = 6s²
SA = 6 × 2.5² = 37.5

Calculator Click What You See Comment
clear blinker clears screen
6 × 2.5 square 6*2.5² SA = 6s²
enter 37.5 Answer
Cube


Question
The side of an ice cube is 2.5 centimeters.
What is its volume?

Answer
15.625 cubic centimeters

Answer Process
V = s³
V = 2.5³ = 15.625

Calculator Click What You See Comment
clear blinker clears screen
2.5 power 3 2.5³ V = s³
enter 15.625 Answer
Cube


Question
The surface area of a large ice cube is 216 square centimeters.
How long is its side?

Answer
6 centimeters

Answer Process
s = SA÷6
s = 216÷6 = 6

Calculator Click What You See Comment
clear blinker clears screen
2nd square root 216 ÷ 6 216÷6

s = √SA÷6
enter 6 Answer
Cube


Question
The volume of a large ice cube is 343 cubic centimeters.
How long is its side?

Answer
7 centimeters

Answer Process
s = ³V
s = ³343 = 7

Calculator Click What You See Comment
clear blinker clears screen
2nd root 343 ³343 s = ³V
enter 7 Answer
Cube


Question
The surface area of a large ice block is 13824 square centimeters.
What is its volume?

Answer
110592 cubic centimeters

Answer Process
s = SA÷6
s = 13824÷6 = 48

V = s³
V = 48³ = 110592

Calculator Click What You See Comment
clear blinker clears screen
2nd square root 13824 ÷ 6 13824÷6
s = √SA÷6
enter 48 s
48 power 3 48³ V = s³
enter 110592 Answer
Cube


Question
The volume of a large ice cube is 729 cubic centimeters.
What is its surface area?

Answer
486 square centimeters

Answer Process
s = ³V
s = ³729 = 9

SA = 6s²
SA = 6 × 9² = 486

Calculator Click What You See Comment
clear blinker clears screen
2nd root 729 ³729 s = ³V
enter 9 s
6 × 9 square 6*9² SA = 6s²
enter 486 Answer
Cube


Practice – Questions
1.  The side of an alphabet cube is 8.7 centimeters.  What is its surface area?

2.  The side of an alphabet cube is 8.7 centimeters.  What is its volume?

3.  The surface area of a large alphabet cube is 3750 square centimeters.  How long is its side?

4.  The volume of a large alphabet cube is 4096 cubic centimeters.  How long is its side?

5.  The volume of a large alphabet cube is 6859 cubic centimeters.  What is its surface area?


Practice – Answers
1.  454.14 square centimeters

2.  658.503 cubic centimeters

3.  25 centimeters

4.  16 centimeters

5.  2166 square centimeters

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