1A large plywood box has a volume of 1440 ft3 Its length is

1)A large plywood box has a volume of 1440 ft3. Its length is 18 ft greater than its height, and its width is 8 ft less than its height. What are the dimensions of the box?

2)A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 100 in3. What is the length of each side of the square piece of cardboard?

Solution

Let the height be h ft

Therefore width,w= h-8 feet and length ,l= h+18 feet

And given volume,V=1440ft³

So we get

h(h+18)(h-8)=1440

(h+12)(h-12)(h+10)=0

h=12,-12,-10

h=12 feet

Therefore width , w= 12-8=4 feet

length , l= 12=18=30 feet

Therefore dimension,l*w*h=30feet*4feet*12feet