Question about calculating area and volume

In summary, the conversation discusses the difference between calculating the volume of a 3D figure and the area between two curves in the xy-plane. While the volume calculation involves rotating a function around the y-axis, the area calculation is based on the sum of whisker-thin rectangles between the curves. It is clarified that this is not a surface area calculation since it is not a three dimensional problem. The importance of calculating area is mentioned to be understood later.
  • #1
Miike012
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When calculating the volume of say y = x^3 rotated around the y-axis from -2<=x<=2 I am the calculating a space occupied by a 3D figure... but when I am calculating the area between say y = x^3 and y=(-x)^3 from 0<= y <=8 what exactly is this area? is it surface area?
 
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  • #2
It's the sum of the areas of all those whisker-thin rectangles, each of height equal to the vertical distance between the curves, viz, x^3 - (-x)^3, and of horizontal width equal to dx or Δx. So it's an area on the x-y plane, a flat area. You could call it a surface area, if you wish, but then all areas could be considered surface areas. couldn't they?
 
  • #3
Miike012 said:
When calculating the volume of say y = x^3 rotated around the y-axis from -2<=x<=2 I am the calculating a space occupied by a 3D figure... but when I am calculating the area between say y = x^3 and y=(-x)^3 from 0<= y <=8 what exactly is this area? is it surface area?
No, there is no "surface" are because this is not a three dimensional problem. It is simply area in the xy-plane.
 
  • #4
I guess ill figure out the importance of calculating area later because right now I don't see it..
 

1. How do I calculate the area of a rectangle?

To calculate the area of a rectangle, you multiply the length by the width. The formula for area is A = l * w, where A is the area, l is the length, and w is the width. Make sure to use the same units for both length and width, such as inches or centimeters.

2. What is the formula for finding the volume of a cube?

The formula for finding the volume of a cube is V = s^3, where V is the volume and s is the length of one side of the cube. This formula can also be used for finding the volume of a square prism, where s represents the length of one side of the base and h represents the height.

3. How do I calculate the area of a circle?

To calculate the area of a circle, you can use the formula A = π * r^2, where A is the area, π is a constant value of approximately 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to its edge.

4. What is the difference between volume and surface area?

Volume is the amount of space occupied by an object, while surface area is the total area of all the surfaces of an object. Volume is measured in cubic units, while surface area is measured in square units. For example, the volume of a cube is how much space it takes up, while the surface area is the total area of all six sides of the cube.

5. How do I convert units when calculating area and volume?

When converting units, make sure to use conversion factors. For example, to convert from inches to feet, you would multiply by 1 foot/12 inches. To convert from centimeters to meters, you would multiply by 1 meter/100 centimeters. Make sure to cancel out units when using conversion factors to ensure the correct unit is obtained in the final answer.

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