By what percentage will the volume of a cube increase if its length is increased by 20 percent, the width is increased

By what percentage will the volume of a cube increase if its length is increased by 20 percent, the width is increased by 30 percent, and the height is decreased by 10 percent?

Let the length of the edge of the cube be t cm. We expressed the length of the edge in centimeters, but it was possible to take any other unit of measurement of length.

Then the volume of the cube is t ^ 3 cm³.

The length of the cube was increased by twenty percent, that is, by twenty hundredths. Let’s find out what the length of the resulting rectangular parallelepiped is equal to.

t + 0.20 * t = 1.2t (cm)

The width of the cube was increased by thirty percent, that is, by thirty hundredths. Let’s find out what the width of the resulting rectangular parallelepiped is.

t + 0.30 * t = 1.3t (cm)

The height of the cube was reduced by ten percent, that is, by ten hundredths. Let’s find out what the height of the resulting rectangular parallelepiped is.

t – 0.10 * t = 0.9t (cm)

Now we can find the volume of the resulting rectangular parallelepiped. To do this, we need to multiply its length, width and height.

1.2t * 1.3t * 0.9t = (1.2 * 1.3 * 0.9) * t ^ 3 = 1.404 * t ^ 3 (cm³)

Let’s find out how many cm³ the volume of the resulting rectangular parallelepiped is larger than the volume of the cube. To do this, you need to make up the difference.

1.404 * t ^ 3 – t ^ 3 = (1.404 – 1) * t ^ 3 = 0.404 * t ^ 3 (cm³)

Now let’s find out how many percent the volume of the resulting rectangular parallelepiped is greater than the original volume of the cube.

(0.404 * t ^ 3) / t ^ 3 * 100% = 0.404 * 100% = 40.4%

We found out that the volume of the resulting rectangular parallelepiped is 40.4% larger than the original volume of the cube.

Answer: 40.4%.