Pyramid and prism??
Question by keiryuuyukito: Pyramid and prism??
Hi i have a question which is giving me problems at the moment.
A greenhouse consists of a pyramid on top of a prism.
The cross section of the prism and the base of the pyramid is a regular octagon. Each side of the octagon is 0.80m long. The height of the prism is 1.73m and the height of the pyramid is 0.68m.
Calculate the volume of the greenhouse give your answer to 3 sig figures.
So imagine an octagon base with height of 1.73 and on top is octagon pyramid which is 0.68m high.
I don’t know how to work it out. Can someone please help me? I would be very grateful!!
Best answer:
Answer by psbhowmick
The formula for area of a regular polygon of ‘n’ sides with each sides measuring ‘a’ units is
A = 0.25*n*a^2*cot(π/n)
Here both the prism and base of pyramid is octagonal.
So, n = 8.
Also, a = each side = 0.8
So, basal area = A = 0.25*8*0.8^2*cot(π/8) = 3.090 m^2
Now, volume of prism
= Basal Area*Height
= 3.090*1.73 m^3
= 5.3457 m^3
and volume of pyramid
= Basal Area*Height/3
= 3.090*0.68 m^3
= 2.1012 m^3
So total volume of the green house is (5.3457 + 2.1012) = 7.4469 m^3.
Rounding off to 3 significant figures, the volume is 7.45 m^3.
What do you think? Answer below!
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