The two edges of the box are 6 and 4, and the volume of the box is 240. Find the surface area of this box.

The volume of a rectangular parallelepiped is found by the formula:

V = A * B * C;

where A and B are the sides of the base of the parallelepiped, and C is the height.

By the condition of the problem, A = 6, and B = 4. Find the value C.

C = V / (A * B).

C = 240/6 * 4 = 240/24 = 10.

We find the surface area of ​​the parallelepiped, which is expressed by the formula:

Spov. = S side. + 2Sn .;

Sosn. = A * B = 6 * 4 = 24.

S side. = Psn. * H, where

Basis perimeter of the base.

Posn = (A + B) * 2 = (6 + 4) * 2 = 20.

H is the height of the parallelepiped, which is 10.

Find S side. :

S side. = Psn. * H = 20 * 10 = 200

Substitute the values ​​into the formula and find the side surface:

Spov. = S side. + 2Sb. = 200 + 2 * 24 = 200 + 48 = 248.

Answer: Sпов. = 248.