Let f be the function that determines the area of a circle (in 
square cm) that has a radius of r cm. That is, f(r) represents the area of a circle (in square cm) that has a radius of r cm.

Use function notation to respond to each item below. A circle has a radius of 28 cm. A second circle has an area that is 54 square cm greater than the first circle's area. Represent the area of the second circle.



The area of a circle is given by the formula:

\[
A = \pi r^2
\]

Let \( f(r) \) represent the area of a circle as a function of its radius \( r \). Therefore, we have:

\[
f(r) = \pi r^2
\]

For the first circle with a radius of 28 cm, the area is:

\[
f(28) = \pi (28)^2 = 784\pi \ \text{square cm}
\]

Now, let the area of the second circle be represented as \( f(r_2) \). We know that the area of the second circle is 54 square cm greater than the area of the first circle, so:

\[
f(r_2) = f(28) + 54 = 784\pi + 54
\]

Thus, the area of the second circle is \( 784\pi + 54 \ \text{square cm} \).

Would you like further details or clarifications on any of these steps? 

Here are 5 related questions to expand your understanding:
1. What is the exact area of the first circle in square centimeters, using \( \pi \approx 3.14 \)?
2. How can we find the radius \( r_2 \) of the second circle from its area?
3. How would the formula change if the radius were expressed in terms of a different unit, like meters?
4. Can you represent the difference between the areas of two circles in terms of their radii?
5. How does the area of a circle change as the radius is doubled?

**Tip**: The area of a circle grows quadratically with the radius, meaning if the radius doubles, the area becomes four times larger.

Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f(r) represents the area of a circle (in square cm) that has a radius of r cm. A circle has a radius of 28 cm. A second circle has an area that is 54 square cm greater than the first circle's area. Represent the area of the second circle.

Learn how to calculate the area of a second circle with a radius of 28 cm, where its area is 54 square cm greater than the first circle's area. This solution involves the use of the formula A = πr² and basic algebraic manipulation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation