Question

A cuboid has it's longest diagonal as 18cm and a square base of side 8cm, calculate the surface area and volume of the cuboid

Answer 1

I don't no how to solve this problem

Answer 2

if the height is h, then
8^2 + 8^2 + h^2 = 18^2
h = 14
So the area is 2(8*8 + 8*14 + 8*14)
and the volume is 8^2 * 14

Answer 3

If the dimensions of a rectangular cuboid are a, b and c,
then the length of the space diagonal is:

d = √ ( a² + b² + c² )

Since the base is square then:

a = b = 8 cm

d = √ ( a² + b² + c² )

d = √ ( 8² + 8² + c² )

18 = √ ( 64 + 64 + c² )

18 = √ ( 128 + c² )

Rise both sides to power of two.

18² = 128 + c²

324 = 128 + c²

Subtract 128 to both sides

324 - 128 = c²

196 = c²

c = √196

c = 14 cm

Surface area is:

A = 2 ( a ∙ b + a ∙ c + b ∙ c )

A = 2 ( 8 ∙ 8 + 8 ∙ 14 + 8 ∙ 14 )

A = 2 ( 64 + 112 + 112 )

A = 2 ∙ 288

A = 576 cm²

Volume is:

V = a b c

V = 8 ∙ 8 ∙ 14

V = 896 cm³