What is the area, and its approximate uncertainty, of a circle with radius3.7 x104cm. With ∆r0.05×104 cm
Question
What is the area, and its approximate uncertainty, of a circle with radius3.7 x104cm. With ∆r0.05×104 cm
Solution
The area of a circle is given by the formula A = πr², where r is the radius of the circle.
Step 1: Calculate the area of the circle Substitute r = 3.7 x 10^4 cm into the formula:
A = π(3.7 x 10^4 cm)² = 4.31 x 10^9 cm²
Step 2: Calculate the uncertainty in the area The uncertainty in the area ∆A is given by the formula ∆A = 2πr∆r, where ∆r is the uncertainty in the radius.
Substitute r = 3.7 x 10^4 cm and ∆r = 0.05 x 10^4 cm into the formula:
∆A = 2π(3.7 x 10^4 cm)(0.05 x 10^4 cm) = 1.16 x 10^9 cm²
So, the area of the circle is approximately 4.31 x 10^9 cm² and the uncertainty in the area is approximately 1.16 x 10^9 cm².
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