Find the surface area of a rectangular parallelepiped, its volume and the area of the diagonal section

Find the surface area of a rectangular parallelepiped, its volume and the area of the diagonal section along its three dimensions a, b, c, if: a = 10 cm, b = 22 cm, c = 16 cm.

Let’s find the volume of a rectangular parallelepiped with a base width of 10 cm, a base length of 22 cm, and a height of 16 cm.

V = 10 cm * 22 cm * 16 cm = 3520 cm³.

Find the surface area of the parallelepiped.

S = 2 * (10 cm * 22 cm + 10 cm * 16 cm + 22 cm * 16 cm) = (220 cm² + 160 cm² + 352 cm²) = 1464 cm².

Find the area of the diagonal section of the parallelepiped.

S = 16 cm * √ ((10 cm) ² + (22 cm) ²) = 16 cm * 24.16 cm = 386.56 cm².

Answer: the surface area is 464 cm², the volume is 3520 cm³, the area of the diagonal section is 386.56 cm².