What is the radius of the Brazilian coin that has a circumference of 84.78 mm? Explain your work. Use 3.14 for π.
Answer (2)
Recall the formula for the circumference of a circle: C = 2 π r .
Substitute the given circumference C = 84.78 mm and π = 3.14 into the formula: 84.78 = 2 × 3.14 × r .
Solve for the radius r : r = 2 × 3.14 84.78 .
Calculate the radius: r = 13.5 mm. The radius of the Brazilian coin is 13.5 mm .
Explanation
Problem Analysis We are given the circumference of a Brazilian coin, which is 84.78 mm. We are also given that we should use 3.14 as the value for π . Our goal is to find the radius of the coin.
Recall the Circumference Formula The formula for the circumference of a circle is given by:
C = 2 π r
where C is the circumference and r is the radius.
Substitute the Given Values We can substitute the given values into the formula:
84.78 = 2 × 3.14 × r
Isolate the Radius Now, we solve for r by dividing both sides of the equation by 2 × 3.14 :
r = 2 × 3.14 84.78
Calculate the Radius Calculating the value of r :
r = 6.28 84.78 = 13.5
Therefore, the radius of the Brazilian coin is 13.5 mm.
State the Final Answer The radius of the Brazilian coin is 13.5 mm.
Examples
Understanding the radius of a coin can be useful in various real-life scenarios. For example, if you are designing a vending machine that accepts Brazilian coins, knowing the radius is crucial to ensure the coin fits properly into the machine's coin slot. Similarly, if you are creating a display case for a collection of coins, knowing the radius helps in designing appropriately sized compartments. This concept is also applicable in engineering and manufacturing, where precise dimensions are necessary for creating compatible parts and components.
The radius of the Brazilian coin is approximately 13.5 mm, found by using the formula for the circumference of a circle. We substituted the circumference of 84.78 mm into the formula and calculated the radius by isolating it. The final result indicates that the radius is 13.5 mm.
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