Question

The TSA of cube \[=726c{{m}^{2}}\]. Find the length of the edge of the cube.

Answer 1

Hint: Use the formula for calculating the total surface area of the cube which is \[6{{a}^{2}}\] where \[a\] represents the length of the edge of the cube. Rearrange the terms and then solve by taking the square root to find the length of edge of the cube whose total surface area is given to be \[726c{{m}^{2}}\].

Complete step-by-step answer:
We have a cube whose total surface area is \[726c{{m}^{2}}\]. We have to find the length of the edge of this cube.

We will use the formula relating the length of edge of the cube with the total surface area of the cube, which is TSA of cube \[=6{{a}^{2}}\] where \[a\] is the length of edge of the cube. One must keep in mind that all the edges of the cube are of equal length.

 Let’s assume that the edge of the cube with TSA \[=726c{{m}^{2}}\] is \[a\] cm. Thus, we have \[6{{a}^{2}}=726\].

Dividing the equation on both sides by \[6\], we have \[{{a}^{2}}=\dfrac{726}{6}=121\].
Taking square root on both sides, we get \[a=11\] as the length of edge can’t be a negative quantity.

Hence, the length of the cube whose total surface area is \[726c{{m}^{2}}\] is \[11\] cm.

A Cube is a three dimensional solid object bounded by six square faces, with three meeting at each vertex. The cube is the only regular hexahedron and has \[6\] faces, \[12\] edges and \[8\] vertices.


Note: Total surface area is the amount of two-dimensional space occupied by the given object. It is the result of multiplying two length measures together. It’s necessary to keep the units in mind while finding out the length of the edge. The total surface area has measurements in \[c{{m}^{2}}\], so the length of edge will be measured in cm.