two rectangular boxes are each 9 inches tall both boxes have square bases.the base edge of the larger box is 1.5 times as long as the base edge of the smaller box .then how much larger box holds when compared to the smaller box
2.25 times
volume = area of base * height
height the same
base 1.5*1.5 = 2.25
To find out how much larger the bigger box holds compared to the smaller box, we first need to determine the dimensions of the two boxes.
Let's assume the base edge of the smaller box is x inches. Since the base edge of the larger box is 1.5 times as long as the base edge of the smaller box, the larger box's base edge would be 1.5x inches.
Given that both boxes have square bases, the volume of a rectangular box with a square base can be calculated by multiplying the base area by the height. In this case, the height of both boxes is 9 inches.
For the smaller box:
Base edge = x inches (let's call it side length)
Volume of the smaller box = side length * side length * height
= x * x * 9 cubic inches
= 9x^2 cubic inches
For the larger box:
Base edge = 1.5x inches (let's call it side length)
Volume of the larger box = side length * side length * height
= (1.5x) * (1.5x) * 9 cubic inches
= 20.25x^2 cubic inches
Now, to find out how much larger the bigger box holds compared to the smaller box, we need to compare their volumes.
Difference in volumes = Volume of the larger box - Volume of the smaller box
= 20.25x^2 - 9x^2
= 11.25x^2 cubic inches
So, the bigger box holds 11.25x^2 cubic inches more than the smaller box.