Given a rectangular parallelepiped with measurements 24 cm, 6 cm and 35 cm

Given a rectangular parallelepiped with measurements 24 cm, 6 cm and 35 cm Find: a) the sum of the lengths of all edges; b) the total surface area; c) volume.

Let’s start at the end:

а) The volume of a rectangular parallelepiped is determined by multiplying its height, length and depth:

6 * 24 * 35 = 5040 cm3;

a) Based on the fact that all parallel sides of the parallelepiped are equal in size, and there are only 12 edges in 3 dimensions, then the sum of the lengths of all edges is found by summing each dimension multiplied by 4 or the sum of all dimensions multiplied by 4:

6 * 4 + 24 * 4 + 35 * 4 = 4 * (6 + 24 + 35) = 4 * 65 = 260 cm;

b) The area of ​​the full surface of a rectangular parallelepiped consists of the sum of the areas of all faces, which in turn are rectangles. The area of ​​any rectangle is equal to the product of its two adjacent sides. There are 6 faces in total, each face has a “pair”, that is, we have only 3 pairs of rectangles with different sides. So the area is equal to the sum of all different-sized faces, multiplied by 2:

2 * (6 * 24 + 35 * 6 + 24 * 35) = 2 * (144 + 210 + 840) = 2 * 1 194 = 2 388 cm2.