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vuyile Posted on Feb 27, 2014
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A pyramid with cube base with adges measure 25 centimeters and has perpendicular of 0.1 meters, calculate total volume of the structure in litres

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kakima

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  • Office Equip... Master 102,366 Answers
  • Posted on Feb 27, 2014
kakima
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I assume you mean a square base.

2.0833 litres.

If this is homework, be sure to show your work.

k24674

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  • Office Equip... Master 8,093 Answers
  • Posted on Feb 27, 2014
k24674
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Be careful of the language you use. A cube is a solid.
If I understand correctly, you have a square-based right pyramid. The length of a side of the base of the pyramid is 25 cm or 2.5 decimeters (2.5 dm). The altitude (height) of the pyramid is 0.1 m or 1 dm
The formula for the volume of a right pyramid is given by
V_pyr=(1/3)(area of base)*height
V_py=(1/3)*[(2.5 dm )^2]* (1 dm)= (25/12) dm^3
Since 1 dm^3 =1 Liter
V_pyr=(25/12) L=2.083333....3 L

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1 Related Answer

Anonymous

  • 81 Answers
  • Posted on Jul 06, 2009

SOURCE: how do i perform the calculation of log (base 2)

Yes look you can't enter the base in calculators it's default 10 so use:
log x base y = log x / log y
log (x*y) = log x + log y
log (x/y) = log x - log y
so instead of log 8 base 2 input log 8 / log 2 it's easy
hope you understand :)

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Life is better in the long run when you understand the principles that exercises try to teach you.
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Volume of triangular pyramid

Here is to get you started. To increase the size of the image do a CTRL Plus (+) in your browser.
You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of (1/2)*SQRT(203) or about 7.1239 cm

913b74c4-c453-4afa-be3a-c3e781816e8d.png

You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found), the measure of the second leg is (1/3) the altitude of the equilateral triangle that forms the base. You should find (1/3) m MH= (1/3)* (11/2)*SQRT(3)
bc7a3bcd-ec6e-4936-9887-c6372904fe9f.png

1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).
2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).
3. Total area = area of base + lateral area.
4. Volume= (1/3)(Area of base)* (height of pyramid)
If you can see the details on the screen capture below, fine, Press CTRL + in your browser to increase the size.
1fbf065d-6c1d-440a-9069-783127aa9842.png
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Rather than relying on a calculator, I highly recommend taking the time to practice metric conversions. It is very common for high school and even college professors to try and trick you by, for example, requesting the answer in centimeters when the question is in meters.
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