Answer to Question #148756 in Geometry for solid mensuration

Question

__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)

Answer 1

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

$$V=\dfrac{L}{6}(A_1+4A_m+A_2)$$

where

$A_1$ and $A_2=$ areas of parallel bases

$A_m=$ area of the section midway between $A_1$ and $A_2$

$L=$ the altitude

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

c) 13 000 cm3

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

$$\cot\alpha=\dfrac{x}{a/2}=\dfrac{x+h/2}{m/2}=\dfrac{x+h}{b/2}$$

$$bx=ax+ah$$

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

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

$$A_m=m^2=(16)^2=256(cm^2)$$

c) 256 cm2