Calculating Surface Area of Rotated Functions

In summary, the task is to find the surface area of a solid obtained by rotating the function y = √9 − X^2, −2 ≤ X ≤ 2 about the X-axis. The formula for surface area of a rotated function is given and it can also be visualized by a simple sketch.
  • #1
vinsento
1
0

Homework Statement



Find the surface area of the solid obtained by rotating
y = √9 − X^2 , − 2 ≤ X ≤ 2 about the X-axis.

Homework Equations



∏r^2


The Attempt at a Solution



Y = (9 - x^2)^-1/2
Is that can do like this..
then how bout the power inside the X^2??
 
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  • #2
∏r^2
That formula applies to circles only.

There is a general formula for surface areas of rotated functions. It is possible to derive it, but usually this is not expected for those tasks, so I think the formula is given somewhere.

Alternatively, draw a sketch of the function. Rotated around the x-axis, it is a well-known object where the surface is easy to calculate.
 

Q1: What is surface area and why is it important to determine?

Surface area is the total area of all the surfaces that make up an object. It is important to determine because it helps us understand the physical properties of an object, such as its size, shape, and characteristics.

Q2: How is surface area calculated?

To calculate the surface area of an object, you need to find the area of each individual surface and then add them together. This can be done using various mathematical formulas depending on the shape of the object.

Q3: What are some common units used to measure surface area?

The most common units used to measure surface area are square units, such as square meters, square inches, or square feet. Other units, such as acres or hectares, may also be used for larger areas.

Q4: Why is surface area different from volume?

Surface area is the measurement of the outer surface of an object, while volume is the measure of the space inside an object. Surface area is a two-dimensional measurement, while volume is a three-dimensional measurement.

Q5: How can determining surface area be useful in real-life situations?

Determining surface area can be useful in various real-life situations, such as calculating the amount of material needed to cover a surface, determining the amount of paint needed for a wall, or calculating the surface area of a human body for medical purposes.

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