Answer:
a.[tex]V(x)=x(10-2x)(6-2x)[/tex]
b.[tex]S(x)=4(15-x^2)[/tex]
Step-by-step explanation:
Dimensions of rectangular piece of cardboard=[tex]10\times 6[/tex]
According to question
Length of box,l=10-2x
Breadth of box,b=6-2x
Height of box,h=x
a.
Volume of box=[tex]l\times b\times h[/tex]
Substitute the values in the formula
Volume of box=[tex]x(10-2x)(6-2x)[/tex]
[tex]V(x)=x(10-2x)(6-2x)[/tex]
b.Surface area of box=[tex]2(b+l)h+lb[/tex]
Because the box has no lid
Substitute the values in the formula
Surface area of box=[tex]2(10-2x+6-2x)x+(10-2x)(6-2x)[/tex]
Surface area of box=[tex]2(16-4x)x+60-20x-12x+4x^2[/tex]
Surface area of box=[tex]32x-8x^2+60-32x+4x^2[/tex]
Surface area of box=[tex]60-4x^2=4(15-x^2)[/tex]
Surface area of box, S(x)=[tex]4(15-x^2)[/tex]
