Question #148756
__24. A prismatoid has an upper base of 90%, a lower base of 2100%, an altitude of 100 cm, and a midsection of 120? What is its volume?

a) 7000 cm3
b) 11 500 cm3
c) 13 000 cm3
d) 17 500 cm3

25. 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.

a)144 cm2
b) 240 cm2
c) 256 cm2
d) 400cm2

(with solution pls)
1
Expert's answer
2020-12-08T07:36:16-0500

24. The volume of prismatoid is given by this formula:


V=L6(A1+4Am+A2)V=\dfrac{L}{6}(A_1+4A_m+A_2)

where

A1A_1 and A2=A_2= areas of parallel bases

Am=A_m= area of the section midway between A1A_1 and A2A_2

L=L= the altitude


V=1006(90+4(120)+210)=13000(cm3)V=\dfrac{100}{6}(90+4(120)+210)=13000(cm^3)

c) 13 000 cm3



25. a=12 cm,b=20 cm,h=14 cma=12\ cm, b=20\ cm, h=14\ cm


cotα=xa/2=x+h/2m/2=x+hb/2\cot\alpha=\dfrac{x}{a/2}=\dfrac{x+h/2}{m/2}=\dfrac{x+h}{b/2}

bx=ax+ahbx=ax+ah

x=ahba=12(14)2012=21(cm)x=\dfrac{ah}{b-a}=\dfrac{12(14)}{20-12}=21(cm)

m=a(x+h/2)x=12(21+14/2)21(cm)=16(cm)m=\dfrac{a(x+h/2)}{x}=\dfrac{12(21+14/2)}{21}(cm)=16(cm)

Am=m2=(16)2=256(cm2)A_m=m^2=(16)^2=256(cm^2)

c) 256 cm2



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