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Calculate the Area of a 5cm Radius Circle to 3 Significant Figures
Mathematics
Grade 9 (Junior High School)
Question Content
A circle has a radius of 5 cm. Work out the area of the circle. Give your answer correct to 3 significant figures.
Correct Answer
78.5 cm²
Detailed Solution Steps
1
Step 1: Recall the formula for the area of a circle, which is $A = \\pi r^2$, where $A$ is the area and $r$ is the radius of the circle.
2
Step 2: Substitute the given radius $r = 5$ cm into the formula: $A = \\pi \\times 5^2$.
3
Step 3: Calculate $5^2 = 25$, so the equation becomes $A = 25\\pi$.
4
Step 4: Calculate the numerical value: $25 \\times 3.14159... = 78.5398...$.
5
Step 5: Round the result to 3 significant figures, which gives 78.5 cm².
Knowledge Points Involved
1
Area of a Circle Formula
The formula for the area of a circle is $A = \\pi r^2$, where $\\pi$ is a mathematical constant approximately equal to 3.1416, and $r$ is the distance from the center of the circle to any point on its edge (radius). This formula is used to calculate the total space enclosed by the circle's circumference.
2
Significant Figures
Significant figures are the digits in a number that carry meaningful information about its precision. When rounding to 3 significant figures, we keep the first 3 non-zero digits and adjust the last digit based on the next digit: if the next digit is 5 or more, we round up the last significant digit. This is used to present measurements or calculated values with appropriate precision.
3
Substitution in Formulas
Substitution is the process of replacing a variable in a formula with its given numerical value. In geometry problems, this is used to plug known measurements (like radius) into standard formulas to solve for unknown values (like area or circumference).
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