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A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2 How many of the smaller cubes have paint on exactly 2 sides?
Mranandaadhikari
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What is the sum of the cubes of first 100 whole numbers?
The sum of the cubes of the first 100 whole numbers is 25,502,500.
What is the total number of cubes of any size with integral side lengths in the 5x5x5 cube?
This is a cracking question. [I'm assuming that 'integral side lengths' is intended also to mean integral positions. That is to say, the position vectors of the cubes' vertices should consist only of integer components...such that we are effectively drawing our cube in a 3D grid. If this was not a condition, the answer would be infinity.] So then: first, there are 53 = 125 1x1x1 cubes. Then 43 = 64 2x2x2cubes. 33 = 27 3x3x3 cubes. 23 = 8 4x4x4 cubes. And, stunningly, 13 = 1 5x5x5 cube. So far we have 225 cubes. That would not be interesting. But we have only counted the cubes with edges parallel to the edges of the main cube. Suppose there are some more cubes formed by diagonal lines? Since edge lengths and vertex positions both have to be integral, and we are working in 3 dimensions, we are actually looking for Pythagorean quadruples - integer solutions to a2 + b2 + c2 = d2 Up to now we have only used trivial solutions like this: 52 + 02 + 02 = 52 Our edges have only moved in one dimension. We might consider edges that move in two dimensions, using the smallest Pythagorean triple: 32 + 42 + 02 = 52 But diagonal edges of length five are clearly not going to fit. So introduce the third component, and we find this: 12 + 22 + 22 = 32 By using diagonal edges it is possible to constuct a few more valid 3x3x3 cubes. It turns out, I think, that four of these can be formed. So we have 229 cubes in total.
What is the Derivation of formula of volume of cuboid?
In the case of a rectangular cuboid, I would say that the volume is simply DEFINED to be length x width x height. The volume of other, more complicated shapes, can then be derived, based on this basic definition. But you do need to have a starting point, i.e., "How is volume even defined in the first place?"Just to show that this definition makes sense, think of a rectangular cuboid as having integer values for length, width, and height. In that case, you can divide it into unit cubes (cubes of side length 1), and it is easy to see (basically, by counting the unit cubes) that the number of unit cubes will be length x width x height - IN THIS SPECIAL CASE.
Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism. How are the surface areas of the figures related?
The ratios of areas are the squares of the ratio of lengths (and the ratio of volumes are cubes of the ratio of lengths). As the perimeter of the second is twice the perimeter of the first, each length of the second is twice the length of the first, and so the ratio of the lengths is 1:2 Thus the ratio of the areas is 1²:2² = 1:4. Therefore the surface area of the larger prism is four times that of the smaller prism.
What is a relation in which each first coordinate is paired with exactly one second coordinate?
Those conditions satisfy the conditions of a function.
What are the first seven cubes?
1,8,27.64.125, 216 and 343 are the first seven cubes.
What is the sum of the cubes of first 100 whole numbers?
The sum of the cubes of the first 100 whole numbers is 25,502,500.
First he used 25 cm cubes to make the base. He put 3 more layers of cubes on top of the first layer of cubes. What is the area ot the prism he built?
what is the answer and how did you get it
When was scenery first painted?
Scenery was first painted during the Renaissance.
If there is 1 cube in the first solid and 6 cubes in the second solid and 15 cubes in the third solid how many cubes are in the eighth solid?
If you have one cube in the first solid than six cubes in the second solid and than fifteen cubes in the third solid, than you would get 215 cubes in the eighth solid.
How do you get bubbles out of ice cubes?
Boil it first
Jerry built a rectangular prism out of base10 blocks first he used 25cm cubes to make the base he put 3 more layers of cubes on top of the first layer of cubes what is the volume of the prism he buit?
8.33
Which is smaller 0.45 kg or 0.456 kg?
The first represents a smaller value (but is not necessarily smaller). 0.45 kg has exactly 6 grams less mass; but a 0.456 kg block of gold would be much smaller than a 0.45 kg marshmallow.
Who painted the first self-portrait?
Davinci painted... "The Mona Lisa".
Jerry built a rectanglrar prism out of 10 base blocks first he used 25 cm cubes to make the base he put three more layers of cubes on top of the first layer of cubes what was the volume of the prism?
25x4=100
Would ice cubes melt in hot water first or will the ice cubes freeze the water first?
If you put ice cubes in a bowl or whatever of hot water, the ice cube is sure to melt when put so says science.
When was First Baptist Church of Painted Post created?
First Baptist Church of Painted Post was created in 1915.
