# Length, Area, and Volume

### Definitions ### Length

The distance between two points ### Area

The amount of space taken up by a shape ### Volume

The space in a 3 dimensional shape

### Formulas

Length: find the distance between two objects

Area: Multiply the lengths of both sides of the shape

Volume: Multiply the lengths of all three sides

### Practice Problems

1) If a man walked up 10 stairs which are each half a foot tall, how much higher is the man from his initial position in inches?

2) If the athlete ran 30 feet forward and then 10 feet backwards how many feet did he run?

3) There is a dogwood tree which is 5 feet tall. There is also a oak tree which is 10 feet taller than the dogwood. If there is a pine tree which is 2 feet smaller than the oak wood tree, how tall is the oak wood tree?

4) If a rectangle has sides of 12 ft and 5 ft what is the area of the rectangle?

5) If a tennis field is 78 ft by 36 ft, what is the area of the field (CALC) ?

6) If a there is one square which has sides of 9 ft and there is a rectangle within the square which has sides of 7 ft and 5 ft, what is the area in the square which is not in the rectangle?

7) If a pool is 6 ft by 10 ft by 5 ft what is the volume of the pool?

8) If a sandbox(rectangular prism) has a volume of 185 ft cubed and the area of one face of the sandbox is 37 ft squared what is the length of the one side not included in the plane.

9) if a rectangular cake is 10 in by 3 in by 7 in, what is the volume of the cake?

HINT: Remember to include units (when doing area you multiply ft x ft = ft squared and for volume ft x ft x ft = ft cubed)

1. 10 * 6 in = 60 in

2. 30 ft + 10 ft = 40 ft

3. 5 ft + 10 ft - 2 ft = 13 ft

4. 12 ft x 5 ft = 60 ft^2

5. 78 ft * 36 ft = 2808 ft^2

6. ( 9 ft x 9 ft ) - ( 7 ft x 5 ft ) = 46 ft^2

7. 6 ft x 10 ft x 5 ft = 300 ft^3

8. 185 ft^3 / 37 ft^2 = 5 ft

9. 10 in x 3 in x 7 in = 210 in^3