A cuboid with a square base surface has the diagonal square root of 118 cm and the longest edge length 10 cm. How big is the volume?

Question

A cuboid with a square base surface has the diagonal square root of 118 cm and the longest edge length 10 cm. How big is the volume?

Answer 1

ΔAGC is the right triangle (face DHGC is ⊥ to the base ABCD, therefore, GC⊥AC).

AG = √188 (hypotenuse)

GC = 10 (one leg)

Calculating AC (2nd leg) from ΔAGC:

AC² = 188 - 100 = 88 → Pythagorean theorem

ΔADC is the right triangle (base is a square)

AD = DC = a → legs

AC → hypotenuse

AC² = 2a²

a² = AC²/2 → the area of the base of cuboid

h = GC = 10 → height of cuboid

Calculating the volume of cuboid:

V = a² • h = (88/2) • 10 = 440 (cm²)

P.S.

I made a picture but it was too large to meet the limitations of the posts.

ABCD is the square base of cuboid.

EFGH is the top square, which is parallel to the base.