Question

What is the volume of a certain cube? (1) The sum of the lengths of the edges of the cube is 36. (2) The surface area of the cube is 54.

Answer 1

Answer:

(1) The sum of the lengths of the edges of the cube is 36.

A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3

Volume = 3*3*3 = 27

(2) The surface area of the cube is 54.

A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)

6s^2 = 54

s = 3

Volume = 3*3*3 = 27

Step-by-step explanation:

All you need to uniquely define a cube is any one measurement - length of a side/edge, area of a surface, volume etc. If you have any one of them, you can uniquely determine the others. So each statement alone is sufficient here.

To show how,

(1) The sum of the lengths of the edges of the cube is 36.

A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3

Volume = 3*3*3 = 27

(2) The surface area of the cube is 54.

A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)

6s^2 = 54

s = 3

Volume = 3*3*3 = 27