First find the volumes and their ratio (beter the bigger to the smaller ratio).
Do not forget : 900 x 1.6 = 90 x 16
1/2 of 1/2, i.e. 1/4 is cut; 3/4 remains. Look at ry1 .
Triangular, is it not? .
First find the area of the equilateral triangle . Its base and height are 5 cm. and 4.3 cm. respectively. You need to multiply these and then
divide by 2.
Then multiply the area by 9 which is the height of the prism (equilateral triangles will be treated as the bases).
There are 4 rectangles and a trapezoid . Area of a rectangle = length x width
Area of a trapezoid = (Legth of bottom (15 cm.) + length of top (7.5 cm.)/2 x height (24 cm.) (in our case 22.5 x 12)
Since the 4 rectangles all have equal heights, find the sum of all lengths and multiply with this height (286.4 cm^{2}) .
The height of the equilateral triangle is given. So are the sides of the rectangles .
We get the average of 1, 3/4 and 1/2 for the remaining parts which ( the average) is 3/4 .
We have also to consider the factor 1/2 due to change of the shape (basic two dimensional form) from a rectangle to a right triangle .
The answer is easy to guess . We have not generalized to any pyramid yet, but we have to leave something for the future.
3/8 - 1/3 = 9/24 - 8/24 = 1/24 .
Do remember that the base is a rectangle .
5x9 + 5x7 + 9x7 + ... = 143 + ... = ...
(1/3) x 20 x 20 x 17.3 = ... .
Since the heights of all prisms are the same, it is enough to find the sum of the base areas of each rectangular prism and multiply this by the
step height.
The base area of the lowest is 20 m. x 20 m. = 400 m^{2} . The next has 18 m. x 18 m. and so on.
Written in the reverse order is the sum 2^{2} + 4^{2} + 6^{2} + ... + 18^{2} + 20^{2} = 1540
This time the height of each step is 17.3/50 = 0.346 m.
The top step has a square base of 20/50 = 2/5 m. side length. And by each step side length increases by 2/5 m.
This time the height of each step is 17.3/100 = 0.173 m.
The top step has a square base of 20/100 = 2/10 m. side length. And by each step side length increases by 2/10 m. .
Percent relative error for 10 steps is (2664,2 - 2306.7)/2306.7 = 357.5/2306.7 = 0.15 i.e. 15 % .
Add, if you can, two more slices just before and after the middle slice .
look at the figure carefully .
Look at the backs of cubes .
Calculate the volume for one of the given measurs and then try to guess .
Remember, for the place of the circles there is no restriction except that they should be tangent to the sides or the rectange at opposite sides .
Find the radiuses of the circles from the perimeter (long side length) of the rectangle .
Take π = 3.14
More than you guess . Take π = 3.2
It is not a vertical plane .
Sym = same metry = measure
The greatest possible intersection area with a plane ?
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