Find the sum of the areas of all faces of a rectangular parallelepiped if its volume is 720 cm3

| July 24, 2021 | education

Find the sum of the areas of all faces of a rectangular parallelepiped if its volume is 720 cm3, and two edges are 15 cm and 24 cm

In order to find the surface area of ​​a rectangular parallelepiped, first, you need to know the total size of its edges. We know the volume, to find the volume we need to multiply three edges of different dimensions. Accordingly, to find one edge, you need to divide the volume into two known ones:

720: 24: 15 = 30: 15 = 2 (centimeters) – the third rib.

The parallelepiped has 12 faces in total. Each 4 is a combination of values ​​from different dimensions. In turn:

24 * 2 = 48; 48 * 4 = 160 + 32 = 192 (cm2).

24 * 15 = 240 + 120 = 360; 360 * 4 = 1200 + 240 = 1440 (cm2).

2 * 15 = 30; 30 * 4 = 120 (cm2).

Let’s find the total area:

192 + 1440 + 120 = 1752 (cm2).

Answer: 1752 cm2.



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