The function $f(t)$ gives the area of a circle with radius $r$. It can be written in equation form as $f(r)=3.14 r^2$. What is $f(4)$?
A. 25.12
B. 50.24
C. 157.75
D. 19.14
Answer (1)
Substitute r = 4 into the function f ( r ) = 3.14 r 2 .
Calculate 4 2 = 16 .
Multiply 3.14 × 16 = 50.24 .
The final answer is 50.24 .
Explanation
Understanding the problem We are given the function f ( r ) = 3.14 r 2 , which represents the area of a circle with radius r . We need to find the value of f ( 4 ) , which means we need to substitute r = 4 into the function.
Substitution Substitute r = 4 into the function: f ( 4 ) = 3.14 × ( 4 ) 2
Calculating the square Calculate 4 2 :
4 2 = 4 × 4 = 16
Final Calculation Now, multiply 3.14 by 16: f ( 4 ) = 3.14 × 16 = 50.24
Result Therefore, f ( 4 ) = 50.24 .
Examples
Understanding functions like f ( r ) = 3.14 r 2 is useful in many real-world scenarios. For example, if you're designing a circular garden and need to calculate the area to buy the right amount of soil or fencing, you would use this formula. If the radius of the garden is 4 meters, then the area is approximately 50.24 square meters. This helps in planning and resource allocation for various projects involving circular shapes.
