Question #150157
1. A prismatoid has an upper base of 90 cm^2 , a lower base of 210 cm^2 , an altitude of 100 cm, and a midsection of 120 cm^2. What is its volume?

2. Find the midsection of a frustum of a square pyramid if its lower base is 20 cm on a side, its upper base is 12 cm on a side, and the altitude of the frustum is 14 cm.
1
Expert's answer
2020-12-15T17:53:39-0500

A)


A1-upper base

A2-medsection

A3-lower base

Formula of volume of prismatoid:

V=L6(A1+4A2+A3)V={L \over 6} \cdot (A1+4 \cdot A2+A3)

V=1006(90+4120+210)=13000m3V={100 \over 6} \cdot (90+4 \cdot 120+210)=13000m^3

Answer: volume of prismatoid: 13000m313000m^3


B)

u-upper base

l-lower bas

a-altitude

m-midsection edge

A-area of midsection

cotα=xu/2=x+a/2m/2=x+al/2cot\alpha ={ x \over u/2}={x+a/2 \over m/2}={x+a \over l/2}

lx=ux+ualx=ux+ua

x=ualu=12142012=21cmx={ua \over l-u}={{12 \cdot 14} \over 20-12}=21cm

m=u(x+a/2)x=12(21+14/2)21=16cmm={u(x+a/2) \over x}={12(21+14/2) \over 21}=16cm

A=m2=162=256cm2A=m^2=16^2=256cm^2


Answer: midsection is 256cm2cm^2



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