Question

Jay wants to make a box, with no lid (or top), out of a 10" x 6" rectangular piece of cardboard. If Jay cuts squares with dimensions x by x out of each corner of the cardboard, and then folds up the corners to make an open box, find a function that represents: (a) The volume of the box. (b) The surface area of the box.

Answer 1

Answer:

a.$V(x)=x(10-2x)(6-2x)$

b.$S(x)=4(15-x^2)$

Step-by-step explanation:

Dimensions of rectangular piece of cardboard=$10\times 6$

According to question

Length of box,l=10-2x

Breadth of box,b=6-2x

Height of box,h=x

a.

Volume of box=$l\times b\times h$

Substitute the values in the formula

Volume of box=$x(10-2x)(6-2x)$

$V(x)=x(10-2x)(6-2x)$

b.Surface area of box=$2(b+l)h+lb$

Because the box has no lid

Substitute the values in the formula

Surface area of box=$2(10-2x+6-2x)x+(10-2x)(6-2x)$

Surface area of box=$2(16-4x)x+60-20x-12x+4x^2$

Surface area of box=$32x-8x^2+60-32x+4x^2$

Surface area of box=$60-4x^2=4(15-x^2)$

Surface area of box, S(x)=$4(15-x^2)$