OK this is pretty easy even though it sounds hard.
Step 1. Determine the radius of the hexagon.
* If the cylinder of the pencil was 12 in diameter and the pencil was cut with the least waste, then the corners of the hexagon would touch the original outer surface of the cylinder. Simply put the diameter of the hexagon would be the same as the original cylinder. * If the diameter was 12 in then the radius is 6 in of course! Step 2. Determine the area of the hexagon.
* Short way: We can use the formula Area = 2.598 * radius2 (i.e 2.598 * 36)
* Long way: This way we learn something!! Assuming we are working this out on paper, draw a line from each corner of the hexagon through the center point to the exact opposite corner. * ** You will notice that you now have 6 equilateral triangles. ** Now we have two ways of continuing
** We can find the area of one of those triangles using the formula √3 / 4 * (s * s) where s= length of one side. ** Or we can use another method which is cooler! ** *** draw a line from the center point through the middle of one of the triangles to the mid point of one of the sides. This divides the equilateral triangle in half and gives us two equal sized right triangles.
*** now we should know that the angles of an equilateral triangle always equal 60 degrees. So now we have a right triangle with 3 angles 90, 60, 30 degrees.
*** Now we put the Pythagorean theorem to work for us. We know the length of the hypotenuse (6in) already as it is one of the sides. And we know the length of one of the other sides (3in) as it ends at the mid point of one of the sides. *** Now using the theorem which is usually written a2 + b2 = c2 we already know c=6 and a=3 we need to solve for b.
*** 32 + b2 = 62 *** 9 + b2 = 36 *** b2 = 36 - 9 *** b2 = 27
*** b= √27 ** Now we can find the area of the smaller right triangle because we know all the value of b. The formula is (length x height) / 2 = Area in square units.
** *** (√27 * 3) /2 = 7.794 sq in
** Now if we take the area of our triangle and multiply it by 12 we will know the area of our hexagon! ** *** The Area of our hexagon is 93.53 sq in Step 3. find the volume of the pencil
* Now we multiply the area of our hexagon by the length of the pencil * ** 93.53 * 8 = Volume of our pencil The answer is 748.25 cubic inches! Thats a big pencil!!
Hold it right there. That's not possible. Something's gotta give.The area of a circle = pi R2 = pi (half the diameter)2If the circle has a diameter of 16, then its area is 201.1(rounded).If it has an area of 64, then its diameter is 9.03(rounded).If it has a diameter of 16 and an area of 64, then it's not a circle.
Assuming that the hexagons are regular then in terms of infinite packing both are 100% efficient so there is nothing to choose between them. For finite packing, however, the shape of the overall space becomes relevant and without detailed information about that it is not possible to answer the question.
Diameter is a special type of chord diameter is a chord that goes through the centre of the circle. Diameter is a longest chord of the circle.and Chord is any line segment which connect one point to other at the circumference of the circle is called chord
It is pi*d where d is the diameter of the circle. Since pi is a transcendental number, it is not possible to express its value exactly and so any value used for pi (3.14, 3.14159 or pi to 10 trillion digits) will still lead to an approximate answer.
That's a chord. The longest possible chord is one that passes throughthe center of the circle. That one is called a "diameter" of the circle.
There are infinitely many possible combinations - ranging from tall thin containers to short wide ones.
Yes
It is impossible to tell since there is no such shape.There are hexagons and heptagons and it is not possible t tell which one you could not spell correctly.It is impossible to tell since there is no such shape.There are hexagons and heptagons and it is not possible t tell which one you could not spell correctly.It is impossible to tell since there is no such shape.There are hexagons and heptagons and it is not possible t tell which one you could not spell correctly.It is impossible to tell since there is no such shape.There are hexagons and heptagons and it is not possible t tell which one you could not spell correctly.
Yes
Infinitely many - if you have an infinite supply of the materials from which they are made.
It is not possible to provide a sensible answer since weight depends on the volume of the object. For a cylindrical object it is necessary to have three measures: outer diameter, inner diameter and length. Instead of the diameters you can have radii or circumference, and instead of two diameters you can have one diameter and the thickness. In any case, three measures are required. Only one is given in the question and there is no indication as to what it refers to!
It's possible but usually not. But any two regularones are definitely always similar.
Thirteen separte hexagons have 13x6 sides, or 78 sides. However, it's possible that they have shared borders, so then there would be fewer because you wouldn't count the same side twice if it was shared.
A diameter is not a unit of length and so no sensible answer is possible.
It is possible to tessellate a plane with squares, triangles, and hexagons. To tessellate something means to cover it with repeated use of a single shape, without gaps or overlapping.
Yes
Yes, it is possible