Volume and Surface Area of a Rectangular Prism

Volume and Surface Area of a Rectangular Prism

A = Rectangular Prism 18 c m 3 10 c m 3 4 c m 3 10 x 18 = 180 surface area 4 x 18 = 72 4 x 10 = 40 x 2 = 584 cm 2

B= Rectangular Prism 12 x 6 = 72 10 x 6 = 60 10 x 12 = 120 x 2 = 504 cm 2 Surface 10 cm 3 12 cm 3 6 cm 3

12 * 12 = 144 Surface Area 12 * 5 = 60 * 2 = 528 cm 2 c = Rectangular prism m c 2 1 3 12 cm 3 5 cm 3

B= Rectangular Prism 36 * 2 Surface Area 10 * 36 10 * 2 *2 = 904 cm 2 36 cm 3 10 cm 3 2 3

1) If the volume is the same in all four, why do they have different surface areas? What kind of rectangular prism gives the greatest surface area? in the all the rectangular prisms, they all have the same volume being 720 cm 3. Although, the volume is the same in all the prisms, the surface area would still be majorly different. This is because the volume is the amount of room inside a 3 D shape. surface area is different because it is the total area of space the surface occupies. For example, If we were to have a longer rectangular prism with a smaller height it would be a bigger surface area because it covers more space length wise. Whereas if we were to have a smaller prism with a longer height, the surface area would be smaller because it covers less space. all of our prisms are somewhat different. some are wider and some are thinner. all the shapes have the same volume of 720 cm 3 but different surface areas because we are calculating the dimensions of the shape.

1) Let’s say the rectangular prism is representing an living room. Which one of your designs would be the best shape for a living room (in feet)? Why is the best one? Why would the others not be a good choice? Out of our rectangular prism designs, our b design would be the best shape for a living room. To be a good living room, there should be enough space for people to be able to stand in the room as well as being able to fit furniture and be spacious. our b design would be the best choice for a living room because it has 10 feet in height and 12 feet in length. This is beneficial for a living room because It has height. Having height will be easier for people to get in and out (especially taller people). our design also has 12 feet in length. This is beneficial because it isn’t too long but it is long enough to maintain a good living room. something that might not be so beneficial for our living room is that it lacks width. The room is only 6 feet wide which may be a tight space for some. a trait that this design had and our other designs didn’t have was the height in the

Cereal Box! We got given 4 different dimensions to make a cereal box. All of the dimensions equaled a volume of 240 inches cubed. We had to find out which of the dimensions would fit the most cereal boxes into a cubed create having 36 inches on each side. To find this out, we divided 36 by each of the numbers the dimensions provided for us. The dimensions that would allow us to fit the most cereal boxes into a create are the dimensions of 3 in by 8 in by 10 in. We figured this out by dividing 36/3 to find out that 12 boxes fit the height of the box. we divided 36/8 to find out that 4 boxes that fit the width of the box. Finally we divided 36/10 to find out that 3 boxes fit the length of the box. These answers were higher than the answers we got for the other dimensions as you can see in the following slide of pictures. correct answer findings;

4 - 6 - 10 -our 12 - from 12 the other equations; findings 4