The sum of the lengths of all the edges of the rectangular parallelepiped is 144cm. Its length is 15cm

The sum of the lengths of all the edges of the rectangular parallelepiped is 144cm. Its length is 15cm and the width is 12cm. Find the volume of the rectangular parallelepiped.

You are given a rectangular parallelepiped. The values ​​of its length are known – 15 cm, width – 12 cm and the sum of the lengths of all its ribs – 144 cm.

The volume of a rectangular parallelepiped is a value equal to the product of the length, width and height of the parallelepiped.

The width of the parallelepiped is not enough to find the volume. We will find it from the formula for finding the length of the edges.

the parallelepiped has 4 lengths, 4 widths and 4 heights. Then the length of the edges L is equal to:

L = 4 * a + 4 * b + 4 * c;

L = 4 * (a + b + c). Substitute the values:

144 = 4 * (15 + 12 + c);

27 + c = 36;

c = 9. The height of the parallelepiped is 9 cm.

Volume V is equal to:

V = a * b * c = 15 * 12 * 9 = 1620 cm³.