An open square-based container is made by cutting 4cm 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
+6251 An open square-based container is made by cutting 4cm 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
The dimensions of the box will be, w x w x h.
Each side will be w x h
\(\text{side area } = w h = 4 \\ \\ h = \dfrac 4 w\)
The volume is given by
\(V = w^2 h = 120 \\ \\ w^2\left(\dfrac 4 w\right) = 120 \\ \\ 4w = 120 \\ \\ w = 30 \\ h = \dfrac 4 {30} = \dfrac 2 {15}\)
So the size of the original piece of tin plate that is the bottom is w x w, or 30x30 cm2
+6251 An open square-based container is made by cutting 4cm 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
The dimensions of the box will be, w x w x h.
Each side will be w x h
\(\text{side area } = w h = 4 \\ \\ h = \dfrac 4 w\)
The volume is given by
\(V = w^2 h = 120 \\ \\ w^2\left(\dfrac 4 w\right) = 120 \\ \\ 4w = 120 \\ \\ w = 30 \\ h = \dfrac 4 {30} = \dfrac 2 {15}\)
So the size of the original piece of tin plate that is the bottom is w x w, or 30x30 cm2
