Eliza’s parents are installing an above ground swimming pool in their backyard. The pool is a right circular cylinder with a dia
meter of 18 feet and a height of 7 feet.
Once her parents fill the pool, it will have a depth of 6 feet. What is the volume of water, to the nearest cubic foot, that will be in the pool once it is filled.
(The volume, V, of a right circular cylinder with radius r and height h is given by the formula)
F. 170
G. 1,527
H. 1,781
j. 2,375
K. 6,107
Once her parents fill the pool, it will have a depth of 6 feet. What is the volume of water, to the nearest cubic foot, that will be in the pool once it is filled.
(The volume, V, of a right circular cylinder with radius r and height h is given by the formula)
F. 170
G. 1,527
H. 1,781
j. 2,375
K. 6,107
1 answer:
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This part of the plane is a triangle. Call it 
. We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that 
means 
, so that (4, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 20) are the other two vertices.
Next, we can parameterize the surface by
so that the surface element is
Then the area of is given by the surface integral
Next, we can parameterize the surface by
so that the surface element is
Then the area of