Question

a cuboid has a square base and is 12 cm high if its total surface area is 512 cm^2 find the area of its base

Answer 1

Total surface area - 512 cm²

Height = 12 cm

Define x:

Let the length be x

Form equation:

Total surface = 2(length x length) + 4(length x height)

Total Surface area = 2x² + 4(12x) = 2x² + 48x

Solve x:

2x² + 48x= 512

2x² + 48x - 512 = 0

2(x - 8)(x + 32)  = 0

x = 8 or x = -32 (rejected because length cannot be negative)

Find the length:

Length = x = 8 cm

Find the base area:

Area = Length x Length

Area = 8 x 8 = 64 cm²

Answer: The base area is 64 cm²