The length of all the edges of the rectangular parallelepiped is 332cm, its length is 5 times its width

| September 17, 2021 | education

The length of all the edges of the rectangular parallelepiped is 332cm, its length is 5 times its width, and its height is 6cm more than its length. Find the surface area and volume.

1) The length of all edges of a rectangular parallelepiped is determined by the formula:

L = 4 * (a + b + c).

We know that this value is 332 cm, and its length is 5 times its width, and its height is 6 cm longer than its length. Let’s make the equation:

4 * (5x + x + 5x + 6) = 332.

Let’s expand the brackets:

20x + 4x + 20x + 24 = 332. On the left side of the equation, we perform operations with the variable, and transfer the known number to the right, while changing the sign in front of it to the opposite:

44x = 332 – 24 = 308.

x = 308: 44 = 7 cm – width.

Length = 7 * 5 = 35 cm and height = 35 + 6 = 41 cm.

2) Let’s calculate the volume of this figure:

V = a * b * c = 7 * 35 * 41 = 10045 cm³.

3) Surface area:

S = 2 * (ab + bc + ac) = 2 * (7 * 35 + 35 * 41 + 7 * 41) = 2 * 1967 = 3934 cm².



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