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How much will the surface area increase if the cube is cut in half?
Wiki User
∙ 13y ago
First, picture a cube one inch on a side.
Each side is one square inch; Six square inches total of SURFACE AREA .
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SCENARIO #1
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A slice (either vertical or horizontal) will add TWO (2) more sides, each being an additional square inch, for a sum total of eight (8) square inches.
An increase of 2 sq. in. over the original six (6) sq. in. is an increase of 33 percent. So, for vertical or horizontal halving, the formula is, as follows:
[ORIGINAL SURFACE AREA times 1.33]
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SCENARIO #2
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But if you halve the cube on a diagonal, the resultant new surfaces will be oblong, measuring 1" by 1.414" (the Square Root of two) adding almost another square inch of surface area.
2 x ( 1 x 1.414) = 2.828 square inches
The total SURFACE AREA is now 8.828 (when halved on the DIAGONAL).
This is an INCREASE of 47.13333 percent.
Resultant formula:
[ORIGINAL SURFACE AREA times 1.4713]
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THEREFORE
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FINALLY, the answer to your question is somewhere between these two extremes, because your cut will be neither a perfect vertical cut, nor a perfect diagonal cut.
Wiki User
∙ 13y ago
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What will happen to the total surface area and the volume of a cube if its each side is halved?
Surface Area: The area of one side is s2, where s is the length of 1 edge of the cube. So the total area is 6s2. If the edge length is half, the new cube area is 6(s/2)2 = 6s2/4, So the new surface area is the original area divided by 4.The volume of the cube is s3. If the edge length is half, the new cube volume is (s/2)3. = (s)3/8. So the new volume is the original volume divided by 8.
What is half a cube called?
half of a cube is called a tetrahedron
What will be the total surface area of a cone whose radius is 2r and slant height is half?
Total surface area = (piradius2)+(piradius*slant length)
What is meant by a symmetry of the cube?
You ether cut it in half or fourths or eighths(do you get the idea?)
How do you figure the square footage of a dome?
Tricky. You need to flatten out the surface to work it out. Depends on the shape - if it's like a hemisphere then you can use the properties of a sphere - volume = 4/3 Pi R3 and surface area = 4 Pi R2 so if your dome is like half a sphere then its surface area = 2 Pi R2 and you can measure the radius R so can work it out!
Is derivative of cube volume surface area of the cube?
No, it is not. It is half of it.
Why is the half cube has more surface area than cube?
because
Can you divide the surface area of a cube in half to get the surface area of a triangular prism?
Yes it is possible.
What is the surface area of a cube with an edge length of 5 and one half yards?
The surface area of a cube with an edge length of 5.5 yards is: 181.5 square yards.
If a cube with a 5 inch side length is sliced in half what is the surface area of the two pieces?
surface area of each piece would be 100 sq.inch
What will happen to the total surface area and the volume of a cube if its each side is halved?
Surface Area: The area of one side is s2, where s is the length of 1 edge of the cube. So the total area is 6s2. If the edge length is half, the new cube area is 6(s/2)2 = 6s2/4, So the new surface area is the original area divided by 4.The volume of the cube is s3. If the edge length is half, the new cube volume is (s/2)3. = (s)3/8. So the new volume is the original volume divided by 8.
What is the surface area in square inches of a cube that has edges of eight and one half inches?
It is 6*8.5^2 = 433.5 square inches.
If you cut a cube in half will the combined surface area of the two halves be more or less?
Yes it will be less because if you take a net of a cube and find the surface area it would be for example 30cm2 and if it was cut in half it would be 15cm squared so its smallerCORRECT ANSWER:Neither. It will be more in area because although you have made two halves of a cube, you have added a new exposed side on each of the halves, thus making 2 sides the same size as the cube. It will lessen by half the area on 4 of the sides which are bisected. So you get the same area that you started with. The above formula is close, but did not account for the other half. Hooweestiki.==========================THE ANSWERS ABOVE ARE WRONG.==========================Here's why...First, picture a cube one inch on a side.Each side is one square inch; Six square inches total of SURFACE AREA .-------------------SCENARIO #1-------------------A slice (either vertical or horizontal) will add TWO (2) more sides, each being an additional square inch, for a sum total of eight (8) square inches.An increase of 2 sq. in. over the original six (6) sq. in. is an increase of 33 percent. So, for vertical or horizontal halving, the formula is, as follows:[ORIGINAL SURFACE AREA times 1.33]-------------------SCENARIO #2-------------------But if you halve the cube on a diagonal, the resultant new surfaces will be oblong, measuring 1" by 1.414" (the Square Root of two) adding almost another square inch of surface area.2 x ( 1 x 1.414) = 2.828 square inchesThe total SURFACE AREA is now 8.828 (when halved on the DIAGONAL).This is an INCREASE of 47.13333 percent.Resultant formula:[ORIGINAL SURFACE AREA times 1.4713]-------------------THEREFORE-------------------FINALLY, the answer to your question is somewhere between these two extremes, because your cut will be neither a perfect vertical cut, nor a perfect diagonal cut.
Why isn't the surface of a hemisphere not half the surface area of a sphere?
The surface area of a semicircle has the round surface which is half a sphere and also has the flat surface which is a circle.
How do you find SA ratio with volume ratio?
The surface-area-to-volume ratio also called the surface-to-volume ratio and variously denoted sa/volor SA:V, is the amount of surface area per unit volume of an object or collection of objects. The surface-area-to-volume ratio is measured in units of inverse distance. A cube with sides of length a will have a surface area of 6a2 and a volume of a3. The surface to volume ratio for a cube is thus shown as .For a given shape, SA:V is inversely proportional to size. A cube 2 m on a side has a ratio of 3 m−1, half that of a cube 1 m on a side. On the converse, preserving SA:V as size increases requires changing to a less compact shape.
How to show that the rate of change of the volume of a cube with respect to the length of its edges is equal to have the surface area of the cube?
If the length of an edge is x, the volume is x3 To find the rate of change of the volume with respect to x, differentiate: d(x3)/dx = 3x2 The area of one face is x2 There are six faces so the total surface area is 6x2 Therefore the rate of change of volume, 3x2 , is half of 6x2 , the surface area.
What is the surface area of a half-sphere with a radius of 10?
Surface area of half a sphere = 2*pi*radius2 Surface area = 200*pi = 628.3185307 square units.
