dave13 wrote:
pushpitkc wrote:
dave13 wrote:
Hello
pushpitkc what is the tempereture under sun today ?
i know that
Surface Area of Cube is \(6a^2\) so plug in 3 into this formula and get 54.
if cube is divided into halves then i get 54/2 = 27
so what am i missing ?
thanks
Hey
dave13It has been hot and humid here
So, the total surface area of a cube is got by adding the individual areas
of the 6 faces of the cube. Now, when the cube is cut in half, there are 5
individual areas that are added in order to give us the surface area of the
figure formed.
Attachment:
Diagram.png
When you add the individual areas you will get the total area, which is \(18 + 9 + 9\sqrt{2} = 27 + 9\sqrt{2}\)
Hope this helps you!
pushpitkc thanks for explanation but i just dont get why you get area of rectanle \(9\sqrt{2}\) and area of two face 18
what faces ?
why you marked you marked some parts in red ?
and how do you get right triangle
This is how I see when cube is cut into halves. So when it is cut I see two equilateral triangles, two rectangles and bottom surface of square shape which occurred as a result of samurai cutting it into halves
Hey
dave13One of the faces(flat surface) of the cube is a square.
PropertyIf the side of the square is x, the diagonal of the square is \(x\sqrt{2}\)
So, in the square where the length of the side is 3, the diagonal is \(3\sqrt{2}\)
The triangle has 3 sides - \(3,3,3\sqrt{2}\). This makes the triangle an isosceles
right triangle as the sides are in the ratio \(1:1:\sqrt{2}\)(Not iscoceles)
Each of the right-angled triangle has the area of \(\frac{1}{2}*\) Product of the legs = \(\frac{1}{2}*3*3 = 4.5\)
Therefore, the sum of the areas of both the triangles will be \(4.5*2 = 9\)
Hope this helps you!
surfingpirate - Hope this explanation clears your confusion as well
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