Answer:
81
Step-by-step explanation:
9 x 9 = 81
So, 81 is the perfect square.
Square means L=W
V=62.5=LWH
L=W so
V=62.5=HL^2
SA=2(L^2+2LH)
we have
V=62.5=HL^2
solve for H
divide both sides by L^2
62.5/L^2=H
sub that for H in other equation
SA=2(L^2+2L(62.5/L^2))
SA=2(L^2+125/L)
SA=2L^2+250/L
find minimum of 2L^2+250L^-1
take the derivitive
4L-250L^-2, or 2(2L^3-125)/L^2
find where it equals zero
it equals zero at L=2.5∛4
L=W
if we evaluate 2L^2+250/L at L=2.5∛4, the value is 75∛2
H=62.5/L^2
H=
![\frac{25 \sqrt[3]{2} }{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%20%5Csqrt%5B3%5D%7B2%7D%20%7D%7B4%7D%20)
dimentions are
L=2.5∛4
W=2.5∛4
H=
![\frac{25 \sqrt[3]{2} }{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%20%5Csqrt%5B3%5D%7B2%7D%20%7D%7B4%7D%20)
minimum surface area is 75∛2 in^2 or aprox 94.4941 in^2
Answer:
225 m³ or 225 cubic meters
Step-by-step explanation:
Actually it has 5 sides, the 2 bases, the 3 lateral faces.
The formula for the volume of a triangular prism is: 
Using the given measurements, we get:

The volume of the prism is 225 m³
You would take 175 and multiply it by 0.20 which is 35. The you would subtract 35 from 175 because it is marked down so you would get 140. Next, you would take 140 and multiply it by 0.10 and get 14. Finally subtract 14 from 140 to get your answer which would be $126.