Question

The total area of the six faces of a cubical box is 96 cm². What is the volume of the cubical box?

Answer 1

Ответ:     V куб =  64 см³ .

Пошаговое объяснение:

   S пов = 6a² ;   6a² = 96 ; ----->   a² = 96 : 6 ;  -----> a² = 16 ;   a = √16 =

       = 4 ( см ) ,  ( а > 0 ) .

    V куб = а³ = 4³ = 64 ( см³ ) ;   V куб =  64 см³ .  

   

Answer 2

To find the volume of a cubical box, we need to know the length of one side of the cube. Let's assume that the length of each side of the cube is represented by the variable "s."

The total surface area of the cube is given as 96 cm². Since a cube has six faces of equal area, we can divide the total surface area by 6 to find the area of each face.

Area of each face = Total surface area / Number of faces Area of each face = 96 cm² / 6 Area of each face = 16 cm²

Since each face of a cube is a square, the area of each face can also be expressed as the side length squared.

Area of each face = s² 16 cm² = s²

To find the length of each side (s), we take the square root of both sides of the equation:

√(16 cm²) = √(s²) 4 cm = s

Now that we know the length of each side of the cube (s = 4 cm), we can calculate the volume of the cube.

Volume of a cube = s³ Volume of the cube = (4 cm)³ Volume of the cube = 4 cm × 4 cm × 4 cm Volume of the cube = 64 cm³

Therefore, the volume of the cubical box is 64 cm³.