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A right rectangular pyramid has base dimensions 5m by 3m and a height of 10m.?
A right rectangular pyramid has base dimensions 5m by 3m and a height of 10m. A horizontal cut is made through the pyramid 2m from its apex and this smaller right rectangular pyramid is removed. What is the volume of the remaining piece?
The answer is 49.6m^3
4 Answers
- strangeLv 69 years agoFavorite Answer
The volume of the pyramid is one third the area of the base times the height. In this case, the original pyramid has volume 5*3*10/3 = 50 m^3.
The smaller pyramid is similar to the larger, with a similarity ratio of 2 to 10, or .2. To find the ratio of volumes, we must cube this. So the smaller pyramid is .008 the volume of the larger. That gives us .4 m^3 as the volume of the smaller.
Now, the remaining volume when the small pyramid is removed is 50 - .4 = 49.6 m^3.
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- mazetonLv 49 years ago
Volume of complete pyramid
V = b1*b2*h/3
V - 5 * 3 * 10 / 3 = 50 m3
This volume minus the volume of the pyramid removed will give you the answer
by triangles: 2.5 / 10 = x / 2
"2.5" equals half side of b1 and "x" equals half side of b1 on the pyramid removed
x = 2.5 * 2 / 10 = 0.5 , so the side on the pyramid removed is 2x or 2*0.5 = 1
Every side is 2/10 th of the original side, so V2 = 1*.6*2/3 = 0.4
Volume of remaining piece is 50 - 0.4 = 49.6 m2
- tannieLv 44 years ago
they pick to appreciate, based on the component of canvas offered, how lots you pays. So first you are able to desire to discover the component of the canvas you have. The formulation for looking component of a triangle is (base x height / 2) in actuality that's the component of a rectangle (base x height or length x width) even nonetheless that is 0.5 of it using fact triangles are sections of rectangles. So now which you have the section b*h/2 = 25 squaremeter you are able to now get the fee understanding that for one squaremeter you pay $18 so which you will pay 25 circumstances that for 25 squaremeters. fee = $450