SOLUTION: A pool, rectangular with semicircled ends.Is surrounded by a walkway, same shape. Pool is 3 feet deep, walkway is 4 feet wide. Length of rectangular walkway on top and bottom of di

Question 709639: A pool, rectangular with semicircled ends.Is surrounded by a walkway, same shape. Pool is 3 feet deep, walkway is 4 feet wide. Length of rectangular walkway on top and bottom of diagram is 20 feet, Semicircular shape of walkway on each end ( is 16 feet in length top to bottom.
Find surface area of pool,
volume of pool,
area of walkway.
If you can figure this one out, you are a GOD!!
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
I'm not sure what you mean by "top to bottom", but I assume the rectangular portion of the pool is 20' by 16' and the radius of the semi-circle is 8'. If this is not correct, I'm not a god! If correct, the area of the pool, (Ap), is the area of the rectangle, 20x16, plus the area of a full circle (semi on each end) with a radius of 8'. This yields
(1) Ap = 20*16 + pi*(8^2) or
(2) Ap = 320 + 64*pi.
The volume of the pool, Vp, is the same as any prism, the area of the bottom times the height. This gives us
(3) Vp = 3*(320 + 64*pi) or
(4) Vp = 960 + 192*pi
The sidewalk surrounds this pool, so along the two straight sides of the pool we have 20' by 4' rectangles and the semi-circular ends combined form a "donut" with a inner radius of 8' and an outer radius of 12'. All this adds to get
(5) As = 2*(20*4) + (pi*(12^2) - pi*(8^2)) or
(6) As = 160 + (144*pi - 64*pi) or
(7) As = 160 + 80*pi
The above expressions are exact. The approximate values are
(8) Ap = 521 sq. ft.
(9) Vp = 1563 cu. ft.
(10) As = 411 sq. ft.
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