Question

Find the side of a cube whose surface area is 600 sq. cm

Answer 1

Hint: The surface area of a 3-dimensional object is a measure of the total area that the surface of the object occupies whereas area is the measurement of the size of a 2-dimensional or the flat surface on a plane. The surface area of a cube is the sum of the area of the six squares that covers it.

Complete step-by-step answer:
To find the side of the cube, use the surface area formula for the cube given as \[SA = 6{a^2}\] where ‘a’ is the sides of the cube. A cube is a three-dimensional solid object bounded by six square faces having 8 vertices and 12 edges which is the only regular hexahedron. All sides of the cube are equal.
The surface area of the cube $600{\text{ c}}{{\text{m}}^2}{\text{ }}$
Let the sides of the cube be \[a\]

Substituting the value of surface area as $600{\text{ c}}{{\text{m}}^2}{\text{ }}$in the formula \[SA = 6{a^2}\] to determine the length of the sides of the cube as:
\[
  SA = 6{a^2} \\
  6{a^2} = 600 \\
  {a^2} = \dfrac{{600}}{6} \\
  a = \sqrt {100} \\
   = 10cm \\
 \]
Hence the side of the cube whose surface area is $600{\text{ c}}{{\text{m}}^2}{\text{ }}$is \[a = 10cm\].

Note: Alternatively, the surface area of a cube can also be found by finding the area of each face of the cube and then adding them together, this value will be equal to the surface area of the cube.
\[SA = {a^2} + {a^2} + {a^2} + {a^2} + {a^2} + {a^2}\]
The base unit to measure surface area is the square units.