The function $f(r)$ 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 $f(3)$?
A. 12.14
B. 18.84
C. 28.26
D. 88.74
Answer (1)
Substitute r = 3 into the function f ( r ) = 3.14 r 2 .
Calculate 3 2 = 9 .
Multiply 3.14 by 9 to get 28.26 .
The final answer is 28.26 .
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 ( 3 ) , which means we need to substitute r = 3 into the function.
Substitution Substitute r = 3 into the function: f ( 3 ) = 3.14 × ( 3 ) 2 .
Squaring Calculate 3 2 = 3 × 3 = 9 . So, f ( 3 ) = 3.14 × 9 .
Multiplication Multiply 3.14 by 9 : 3.14 × 9 = 28.26 . Therefore, f ( 3 ) = 28.26 .
Final Answer The value of f ( 3 ) is 28.26 . Comparing this with the given options, we see that option C is the correct answer.
Examples
Imagine you're designing a circular garden with a radius of 3 meters. The function f ( r ) = 3.14 r 2 helps you calculate the area of the garden, which is essential for determining how much soil or how many plants you'll need. In this case, f ( 3 ) = 3.14 × 3 2 = 28.26 square meters. This calculation allows you to plan your garden efficiently, ensuring you have the right amount of materials and plants to fill the space.
