SOLUTION: I need to find the surface area of the inside of a dry pond in the shape of an oval. The length is 107 ft. The Width is 41 ft. And it is 5 ft deep. Please help me find the sufa

Algebra ->  Surface-area -> SOLUTION: I need to find the surface area of the inside of a dry pond in the shape of an oval. The length is 107 ft. The Width is 41 ft. And it is 5 ft deep. Please help me find the sufa      Log On


   

Question 214689: I need to find the surface area of the inside of a dry pond in the shape of an oval. The length is 107 ft. The Width is 41 ft. And it is 5 ft deep. Please help me find the suface area of this oval shaped dry pond.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this in two steps:
1). Find the area of the oval (elliptical) bottom of the dry pool.
2). Find the inside area of the oval-shaped side.
Add these together to get total inside surface area.
1) The area of an ellipse is given by:
A+=+%28pi%29%2Aa%2Ab where a = the length of the semi-major axis and b = the length of the semi-minor axis.
In this pool, the semi-major axis (a) is 107/2 = 53.5ft.
The length of the semi-minor axis (b) is 41/2 = 20.5ft.
A+=+%28pi%29%2853.5%29%2820.5%29
highlight_green%28A+=+3445.5%29sq.ft.
2) The area of the of the iside of the elliptical-shaped pool by multplying the circumference of the pool by the depth of the pool.
The approximate circumference (C) of the elliptical pool is given by:
C+=+2%28pi%29sqrt%28%28a%5E2%2Bb%5E2%29%2F2%29
a%5E2+=+53.5%5E2
a%5E2+=+2862.25
b%5E2+=+20.5%5E2
b%5E2+=+420.25
C+=+2%28pi%29sqrt%28%282862.25%2B420.25%29%2F2%29
C+=+254.55
Now multiply this by the depth of the pool (d+=+5ft.)
C%2Ad+=+%28254.55%29%2A%285%29=highlight_green%281272.75%29sq.ft. This is the area of the inside wall of the pool. Add the two areas to get the total surface area (S) of the inside of the dry pool.
S+=+3445.5%2B1272.75
highlight%28S+=+4718%29sq.ft.