Question

Найти объём куба, если площадь его одной поверхности равна 96 см.кв.

Answer 1

S (площ.поверх) = 6Н^2 , где Н - ребро куба

6H^2=96

H^2=16

H=$\sqrt{16}$=4 (см)

V (объем куба) =H^3=4^3=64 куб.см

Answer 2

1) 96:6=16(см2) - S 1 стороны.

2) 16 - квадрат цифры 4(см) - ребро куба.

3)  4*4*4=64(см3) - объём куба.

Ответ 64 см3 -  объём куба.

Answer 3

Finding the Volume of a Cube with a Given Surface Area

To find the volume of a cube when the surface area of one of its faces is given, we need to use the formula for the surface area of a cube and then solve for the side length. Once we have the side length, we can calculate the volume of the cube.

The formula for the surface area of a cube is S = 6a^2, where S is the surface area and a is the side length of the cube.

In this case, the surface area of the cube is given as 96 cm^2. Let's solve for the side length:

96 = 6a^2

To find the value of a, we can rearrange the equation:

a^2 = 96 / 6

a^2 = 16

Taking the square root of both sides, we get:

a = √16

Therefore, the side length of the cube is 4 cm.

Now that we know the side length, we can calculate the volume of the cube using the formula V = a^3:

V = 4^3

V = 64 cm^3

So, the volume of the cube is 64 cm^3.

Please note that the above calculations are based on the assumption that the given surface area is for one face of the cube. If the given surface area is for the total surface area of the cube (including all six faces), the calculations would be different. However, based on the information provided, we assume that the surface area refers to one face of the cube.

I hope this helps! Let me know if you have any further questions.