Part 1:
A rectangular box is 2 inches high, 3.5 inches wide amd 4 inches long. A cyliner box is 3.5 inches high and has a diameter of 3.2 inches. Use 3.14 for pi. Round to the nearest tenth.
Part 2: whWhich box has a larger volume.
How much bigger is the larger box?
V₁= abc=2•3.5•4 = 28 in³
V₂=A•h=(πD²/4) •h=
=3.14•3.2²•3.5/4=28.15 =28.2 in³
V₂ > V₁
Part 1:
To find the volume of the rectangular box, you multiply its length, width, and height. In this case, the height is 2 inches, the width is 3.5 inches, and the length is 4 inches. So the formula for the volume of a rectangular box is height x width x length.
Volume of rectangular box = 2 inches x 3.5 inches x 4 inches = 28 cubic inches.
Now, to find the volume of the cylindrical box, you need to calculate the volume of a cylinder. The formula for the volume of a cylinder is pi x radius^2 x height. Here, the height is 3.5 inches and the diameter is 3.2 inches, so you can divide the diameter by 2 to get the radius.
Radius = diameter / 2 = 3.2 inches / 2 = 1.6 inches.
Volume of cylindrical box = 3.14 x (1.6 inches)^2 x 3.5 inches = 28.2744 cubic inches.
Part 2:
Comparing the volumes of the two boxes, we find that the volume of the rectangular box is 28 cubic inches, and the volume of the cylindrical box is approximately 28.2744 cubic inches.
Since the volume of the cylindrical box is larger than the volume of the rectangular box, the cylindrical box has a larger volume.
To find out how much bigger the larger box is, you subtract the volume of the smaller box from the volume of the larger box.
Difference in volume = Volume of cylindrical box - Volume of rectangular box
= 28.2744 cubic inches - 28 cubic inches = 0.2744 cubic inches.
So, the larger box is approximately 0.2744 cubic inches bigger than the smaller box.