Question

The surface area of a cube is 326 square meters. How long is each edge?

Answer 1

Hint: Cube is a three dimensional solid object bounded by six square faces and twelve edges of equal length. The area of the one face that is one square is \[{x^2}\] square units. Then the area of 6 faces is 6 times \[{x^2}\] . That is \[6 \times {x^2}\] square units. Using this we can solve this.

Complete step by step solution:
Given that the surface area of a cube is 326 square meters. That is \[A = 326{m^2}\]
Also the area of one square is \[ \Rightarrow {x^2}\] square meters.
By the definition of the cube we have six square faces then the area of the 6 square face is,
 \[ \Rightarrow A = 6 \times {x^2}\] square units.
 \[ \Rightarrow 326 = 6 \times {x^2}\]
 \[ \Rightarrow 6 \times {x^2} = 326\]
 \[ \Rightarrow {x^2} = \dfrac{{326}}{6}\]
Taking square root on both sides we have,
 \[ \Rightarrow x = \sqrt {\dfrac{{326}}{6}} \]
 \[ \Rightarrow x = \sqrt {54.333} \]
 \[ \Rightarrow x = \sqrt {54.333} \]
 \[ \Rightarrow x = 7.37\]
That is, each edge is 7.37 meter.
So, the correct answer is “7.37 meter.”.

Note: We also know that the angles of the cube are at right angles and each of the faces meets the other adjacent four faces. The curved surface area of the cube and lateral surface area of the cube are different. The lateral surface area of a cube is \[4 \times {(edge)^2}\] . The curved surface area of the cube is \[6 \times {\left( {side} \right)^2}\] . The volume of the cube is \[{(side)^3}\] .