The volume of a rectangular parallelepiped is 54 cm. One side of the base is 2 times

The volume of a rectangular parallelepiped is 54 cm. One side of the base is 2 times larger. Base area 18 cm2. Find the total surface area.

One side of the base of the parallelepiped is 2 times larger than the other.

The base of a rectangular parallelepiped is a rectangle.

Let m be one side of the base, then (2 * m) is the other side.

Let’s write the equation of the base area and find the sizes of the sides:

m * 2 * m = 18;

m ^ 2 = 9;

m = 3 cm;

2 * m = 3 * 2 = 6 cm.

Find the height of the parallelepiped:

c = V / (a * b = 54 / (3 * 6) = 3 cm.

We found the dimensions of the parallelepiped, now we find the total surface area:

S = 2 * (a * b + a * c + b * c) = 2 * (3 * 6 + 3 * 3 + 6 * 3) = 2 * (18 + 9 + 18) = 2 * 45 = 90 cm² …