Question

Raymond wants to make a box that has a volume of 360 cubic inches.he wants the height to be 10 inches and the other two dimensions to be whole numbers of inches.how many different sized boxes can he make

Answer 1

the volume of the box is l*w*h, or in this case, l*w*10, and also the volume is 360. so, 10lw=360, meaning l*w=36, so we are looking for whole number factors of 36.

length: 1 2 3 4 6 9 12 18 36
width:36 18 12 9 6 4 3 2 1

there are a total of 9 possible ways to make the base of the box so 9

Answer 2

The number of boxes that can be made are:

9

Explanation:

The volume of a box is given to be: 360 cubic inches.

Height(h) of a box is: 10 inches.

Let the length and the width is denoted by l and w respectively.

Hence, the volume is given by:

Volume=l×w×h=360

l×w×10=360

l×w=36

Hence, the possible dimensions are:

Length(l) 1 2 3 4 6 9 12 18 36

Width(w) 36 18 12 9 6 4 3 2 1

Hence, the number of such boxes possible are : 9

Since there are possible 9 dimensions possible of a box.