Volume and Surface Area of a Rectangular Prism

Volume and Surface Area of a Rectangular Prism

Rectangular Prism #1 ● ● ● Length: 10 meters Width: 9 meters Height: 8 meters Work Volume: 8 x 9 x 10 = 720 meters 3 Work Surface Area : 8 x 9 = 72 meters 10 x 8 = 80 meters 9 x 10 = 90 meters 90+90+80+80+72+72 = 484 meters 2

Rectangular Prism #2 ● ● ● Length: 72 kilometers Width: 10 kilometers Height: 1 kilometers Work Volume: 72 x 10 = 720 meters 3 Work Surface Area : 1 x 10 = 10 kilometers 2 72 x 10 = 720 kilometers 2 1 x 72 = 72 kilometers 2 10+10+720+72+72 = 1, 604 kilometers 2

Rectangular Prism #3 ● ● ● Length: 10 centimeters Width: 2 centimeters Height: 36 centimeters Work Volume: 36 x 2 x 10 = 720 centimeters 3 Work Surface Area : 36 x 2 = 72 centimeters 2 10 x 2 = 20 centimeters 2 36 x 10 = 360 centimeters 2 72+72+20+20+360 = 904 centimeters 2

Rectangular Prism #4 ● ● ● Length: 6 millimeters Width: 20 millimeters Height: 6 millimeters Work Volume: 6 x 20 x 6 = 720 millimeters 3 Work Surface Area : 6 x 6 = 36 millimeters 2 20 x 6 = 120 millimeters 2 6 x 20 = 120 millimeters 2 36+36+120+120 = 552 millimeters 2

Step #5 and #6 5# As you can see each of those rectangular prism has a volume of 7203. But the surface area isn’t the same, that is so because each rectangular prism take a different amount of space. That is so because the closest a rectangular prism looks like a cube, it will have a smaller surface area. The rectangular prism that has the biggest surface area is box 2 because it is flat and most importantly it doesn’t look like a cube. 6# The blue box is representing best a living room because it’s like the normal size of most living rooms around the world because the height is 8 meters, the width is 9 meters and the length is 10 meters. This is why this box is the best to represent a living room. The dimensions are well divided but most important it isn’t squish or isn’t small in height or width. That makes the person living in the house to have a big space to move around the living room. A counter argument for example box 3 because you don’t have a living

Step #7 Cereal box 1 : Volume V = length x width x height v = 4 in x 6 in x 10 in v = 240 inch 3 Cereal box 1 : Volume 3 V = length x width x height v = 3 in x 8 in x 10 in v = 240 inch 3 Cereal box 1 : Volume 3 V = length x width x height v = 4 in x 5 in x 12 in v = 240 inch 3 3 Work for how many boxes fits in the crater: 36 / 4 = 9 36 / 6 = 6 36 / 10 = 3 36 / 3 = 12 36 / 8 = 4 36 / 10 = 3 36 / 4 = 9 36 / 5 = 7 36 / 12 = 3 9 x 6 x 3 = 162 3 x 4 x 12 = 144 9 x 7 x 3 = 189

Dimensions that could fit (work on it for hw) On this question we were given 3 boxes with 3 different measurements. With these measurements we had to find out which box would fit the most in the crate. The dimensions of the crate are all 36 since it’s a square. The first 3 dimensions for the first box is 4, 6, 10. Because we need to see how many of the boxes will fit on each side, to see how many will stack up in the length, width and height (we are finding how many layers of the boxes will fit). The first thing you do is take one dimension and divide 36 by it. The reason we do this is to see how many of the boxes will fit on one side, then you do the rest. Once you divide 36 by each of the dimensions, you have to multiply them together. The multiplied number will give you the amount of boxes that fit the crate. Because we want to see which box will fit the most length width and height wise. Once you find the capacity of the boxes you see which has the most capacity to fit in the big box. We found out that the box C can fit the most boxes.