The length of the rectangular parallelepiped is 90 cm, the width is 25 cm, and the height is 12 cm.

The length of the rectangular parallelepiped is 90 cm, the width is 25 cm, and the height is 12 cm. Find the length of the edge of the cube, the volume of which is equal to the volume of this rectangular parallelepiped. Which of the two figures has more surface area and how much?

Brief record of the task.

Dimensions of the parallelepiped:

a = 90 cm;

b = 25 cm;

c = 12 cm;

V1 =? cm ^ 3;

S1 =? cm ^ 2;

cube dimensions:

a =? cm;

V2 = V1;

S2 =? cm ^ 2.

1. Let’s calculate the volume of a given parallelepiped:

V1 = V2 = a * b * c = 90 * 25 * 12 = 27000 cm ^ 3.

2. Calculate the length of the edge of the cube:

V2 = a ^ 3, 27000 = a ^ 3, a = 30 cm.

3. Define and compare the surface areas of the figures:

1) parallelepiped – S1 = 2 * (a * c + c * b + a * b) = 2 (90 * 12 + 12 * 25 +90 * 25) = 2 (1080 + 300 + 2250) = 7260 cm ^ 2;

2) cube – S2 = 6 * a ^ 2 = 6 * 30 ^ 2 = 5400 cm ^ 2;

3) 7260 – 5400 = 1860 cm ^ 2.

Answer: 1860 cm ^ 2 more surface area of the parallelepiped.