Answer to Question #150157 in Geometry for solid m

Question

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.

Answer 1

A)

A1-upper base

A2-medsection

A3-lower base

Formula of volume of prismatoid:

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

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

Answer: volume of prismatoid: $13000m^3$

B)

u-upper base

l-lower bas

a-altitude

m-midsection edge

A-area of midsection

$cot\alpha ={ x \over u/2}={x+a/2 \over m/2}={x+a \over l/2}$

$lx=ux+ua$

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

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

$A=m^2=16^2=256cm^2$

Answer: midsection is 256$cm^2$