SURFACE AREA & VOLUME

1) A rectangular pool is 60 feet long by 30 feet wide.  The shallow end is 4 feet deep and the deep end is 8 feet deep.  Find the surface area and the volume.

2) A circular spa has a 10 foot diameter and a constant depth of 4 feet deep.  Find the surface area and the volume.

3) A rectangular pool has a swimming area and a diving well.  The swimming area is 75 feet long by 25 feet wide and is 3 feet deep to 5 feet deep.  The diving well is 25 feet long by 25 feet wide and has a constant depth of 10 feet deep.  Find the total volume.  (Hint:  Split the pools, then find the volume of each and add totals.) 


 




 

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FORMULAS

Surface Area (Circle): Radius x Radius x 3.14 (Radius = Diameter / 2)
Surface Area (Rectangle/Square):  Length  x  Width
Volume (Circle/Rectangle/Square): Surface Area x Average Depth x 7.5
Average Depth: (Shallow Depth + Deep Depth) ÷ 2
(Note: Constant Depth = Average Depth)  

EXAMPLE

A rectangular pool is 50 feet long by 20 feet wide.  The shallow end is 3 feet deep and the deep end is 7 feet deep.  Find the surface area and the volume.

 Surface Area = Length  x  Width
 Surface Area = 50 feet  x  20 feet
 Surface Area = 1,000 square feet

 Volume = Surface Area  x  Average Depth  x  7.5
 Volume = 1,000  x  Average Depth  x  7.5
 Average Depth = (Shallow Depth + Deep Depth) ÷ 2
 Average Depth = (3 + 7) ÷ 2
 Average Depth = 10 ÷ 2
 Average Depth = 5
 Volume = 1,000  x  5  x  7.5
 Volume = 37,500 Gallons

ANSWERS

1. Surface Area = 1,800 square feet  Volume = 81,000 Gallons
2. Surface Area = 78.5 square feet  Volume = 2,355 Gallons
3. Total Volume = 103,125 Gallons 

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