Question

an open square-based container is made by cutting 4 cm square pieces out of a piece of tinplate if the volume of the container is 120cm^3 find the size of the original piece of tinplate

Answer 1

Original measures of the tinplate square: x cm * x cm

Measure of thesides of the tinplate after cutting two 4 cm square pieces out of each side: [x - 8]*[x - 8] (this is the base of the container)

Volume of the container =: area of the base * height

area of the base = [x - 8]^2

height = 4 cm

Volume of the container 4*[x - 8]^2 = 120 cm^3

Divide both sides by 4: [x - 8]^2 = 30 cm^2

Extract square root from both sides: [x - 8] = √(30 cm^2)

 [x - 8] ≈ 5.5 cm

x ≈ 5.5cm + 8 cm ≈ 13.5 cm

Answer: the side of the original tinplate square was approximately 13.3 cm