8C.5.3 Surface Area
Every 3d shape has a surface. The total area of that shape is the surface area. If the 3d shape is a polyhedron (something with flat faces) then it is usually pretty easy to find the total area of the surface:
Resources:
- What is a prism? Watch the Prism Video on Youtube if you're not sure. All the prisms we will be looking at in this course are "right prisms"
Assignment:
- Watch the 4 videos shown below and complete your notes before coming to next class.
- Blank Notes Template: 8C.5.3 Surface Area
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Leave a comment to answer the question:
- Imagine a 3d shape. If a hole is drilled through from the top to the bottom, will the surface area be larger or smaller?
In Class Assignment:
- HW 5.3 p180 #3-8, 10, 12, 13, 15
- Constructing prisms from nets and finding their surface area
Comments (16)
Then the hole you drilled would have to be subtracted from the surface area.
That depends on the hight of the shape. If the shape is very short then the surface area will get smaller. If the shape is very tall there will be more surface area around the sides of the hole then there originaly was on the top and bottom of said shape.
The surface area will be smaller. only the area of the hole on the surface wil be subtracted from the surface area, as u only are measuring the outside of the object
i think that the surface area would be larger depending on the size and height of the shape. If the shape was short the it would be the same or maybe less because the surface area gained from the inside of the hole would only be small so it may not make up for the surface area lost making the hole. If the shape were tall then you would gain more sufface area from inside the tube than lost from the hole.
If R2xR2 is less than R2xH, then the total surface area would increase. If R2xR2 is greater than R2xH, then the total surface area would decrease. If R2XR2 = R2xH, then there is no change in the total surface area.
I think that in most cases, the surface area would be bigger or the same, because the piece taken out only shows the top and bottom, but when it is taken out, the inside of the object shows. The thinner the object, the less surface area is gained while the thicker the object, the more surface area is gained.
The surface area would become larger because you have to calculate the surface area of the hole you just drilled through the object. For example if you have an apple and the surface area is 0.1m squared then you core the apple, you have taken a small amount of the surface from the top and bottom but you have increased the surface area by having that inner core the apples new surface area maybe 0.15m squared.
the surface area would get bigger because the area that is subtracted will never equal the increase of surface area in the middle of the shape.
It depends how tall the shape is. If the shape is tall enough the added surface area from the hole will be more than the surface area on the top and bottom that's taken away by the hole. If the shape is short than the area taken away by the hole on the top and bottom will be more than the area added by the hole and the surface area will be smaller.
the surface area would decrease because a piece of the shape was taken out by drilling a whole through it.
If you drilled a hole through a 3D object that was very thin such as a peice of paper, with a large drill bit you would destroy some of the surface area. However, if it was a larger and thicker object such as a block of wood, you would increase the surface area because when you drill the hole through the object you have to calculate for the new surface area of the wall of the core you have just created
It all depends on the thickness of the sides of the 3D shape and the size of the hole drilled. A large hole can decrease the surface area if the object is thin, but we have to take in consideration the height of the 3D shape. Though, everything can change depending if the 3D shape is hollow or not. If the shape is hollow then drilling the hole may increase the surface area because we are exposing the inside surface area.
most likely the surface area will grow because when you drill a hole in you are removing a bit of the shape from both the top and the bottom, but you are probably adding more sides from the hole you have drilled in. Sort of depends how thick the object is. If you make a hole in a piece of paper you losing more surface area then you are gaining
The surface area would be bigger because even though you are getting rid of a bit of the surface area of the shape, when you drill the whole you are also making new sides so that would make more surface area so the surface area would get bigger.