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Which has greater surface area a sugar cube or an equal mass of sugar crystals?
Consider this:If a cube has side length d, then its volume is d3 and its surface area is 6d2.If I cut the cube into 8 smaller cubes by bisecting each edge, then the new side length is d/2, the sum of the volume is 8 * ((d/2)3) = d3, and the surface area is 8 * (6(d/2)2) = 12d2.Therefore, even though the volume stayed constant, the sum of the surface area increased when I cut a larger cube into small cubes. The increase in surface area will be larger and larger as the cube is cut into smaller and smaller pieces. Therefore a sugar cube always has less surface area than an equal mass of sugar crystals.Granulated sugar has more surface area than a sugar cube.
What is a cube is removed from the corner of a larger cube Datermine and explain the relationship between the total surface area of the original larger cube the new figure with the missing portion?
If we remove a cube from the corner then cavity we get to see can be considered in the form of a cuboid room and the room doesn't has roof and front wall because the cube is removed from the corner(you can consider any two surfaces).Let us say the side of larger cube be A then its surface area is 6A2.And we have removed a cube of side a from the corner. After removing we get 4 squares of side a in the cavity and the area is 4 x a2. But the roof and front wall is not there so there is decrease in area by 2 x a2.So, the surface area of new figure is 6A2 + 4a2 - 2a2 = 6A2 + 2a2.So the surface area of new figure is more than the original cube.
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.
As the radius of a sphere gets larger which of the spheres measurements increases more the surface area or the volume?
The volume increases faster. (proportional to the cube of the radius)The surface area increases slower. (proportional to the square of the radius)
How much faster does volume increase compared to surface area?
Hi,In general when something becomes larger, the surface area to volume ratio decreases. The analogy of a cube is indeed a useful way to think about it. I'll try to put it in more general terms.Cubes are a great example to talk about because their surface area and volume are really easy to calculate. The surface area of a cube is the length x the width x the number of sides (six sides, in the case of a cube). The volume of a cube is the length x width x volume.So, say we have a cube with a side length of three. The surface area is going to be 3x3x6 = 54. The volume is going to be 3x3x3 = 27, for a ratio of 54:27, or 2:1//Another contributor does not think you should make a ratio of different dimensions (area and volume)//Surface area increases as the square of a dimension, volume increases as the cube of a dimension.Example:A sphere (ball)Diameter = 1 unitIncrease diameter to twice the size: New diameter = 2Area of new sphere = 4 times the area of the initial sphereVolume of the new sphere = 8 times the volume of the initial sphere
