SOLUTION: What is the volume of a tent with measurements: h=2m b=3m l=? SA (outside of tent)=38m^2 Please explain. Thank you in advance!

Algebra ->  Volume -> SOLUTION: What is the volume of a tent with measurements: h=2m b=3m l=? SA (outside of tent)=38m^2 Please explain. Thank you in advance!      Log On


   

Question 255681: What is the volume of a tent with measurements:
h=2m
b=3m
l=?
SA (outside of tent)=38m^2
Please explain. Thank you in advance!
Found 2 solutions by drk, CharlesG2:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The surface are has the formula:
SA+=+bL+%2B+bh+%2B+2%2AL%2Asqrt%28b%5E2%2Bh%5E2%29
by substitution, we get
38+=+3L+%2B+3%2A2+%2B+2%2AL%2Asqrt%283%5E2%2B2%5E2%29
or
38+=+3L+%2B+6+%2B+2Lsqrt%2813%29
32+=+L%2A%283+%2B+2sqrt%2813%29%29
L+=+32%2F%283+%2B+2sqrt%2813%29%29
--
V = LxWxH
V = 3 x 2 x 32/(3+2sqrt(13))
V = 192/(3+2sqrt(13))
V ~ 18.803 m^3

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
What is the volume of a tent with measurements:
h=2m
b=3m
l=?
SA (outside of tent)=38m^2
Please explain. Thank you in advance!
thinking this is a triangular tent
2 sides for the top, 1 side for bottom, 1 front, 1 back
that is 5 sides
front=back=(1/2)(3)(2)=(1/2)(6)=3 --> total SA 6m^2
((1/2)b)^2+h^2=(width of one of the top sides)^2 let's call it slope^2
((1/2)(3))^2+2^2
1.5^2+4
2.25+4
6.25=slope^2
2.5=slope
top=2*2.5*l=5*l
bottom=3*l
5*l+3*l+6=38
8*l=32
l=4
V=hbl
v=2*3*4=6*4=24 m^3
oh drat, I realized I made an error
volume of the prism standing up right would be area of base times the height
in this case area of one of the triangular sides times the length
V should be 1/2 * base * height * length
V= 1/2 * 3 * 2 * 4
V= 1/2 * 6 * 4
V= 1/2 * 24
V=12 m^3 NOT 24 m^3
sorry