Areas Related to Circles
NCERT Exemplar Ch 10
CBSE_NCERT_EXEMPLAR_CH10
Grade 10
Question:
If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius $R$, then:
$R_1 + R_2 = R$
$R_1^2 + R_2^2 = R^2$
$R_1 + R_2 < R$
$R_1^2 + R_2^2 < R^2$
Step-by-Step Solution
Key Concept: $\\pi R_1^2 + \\pi R_2^2 = \\pi R^2 \\Rightarrow R_1^2 + R_2^2 = R^2$.
Stepwise Solution:
$\pi R_1^2 + \pi R_2^2 = \pi R^2 \Rightarrow R_1^2 + R_2^2 = R^2$. [1.0 Mark]
Marking Scheme:
• Cancelling $\pi$ to get $R_1^2 + R_2^2 = R^2$: 1.0 Mark
Correct Answer: $R_1^2 + R_2^2 = R^2$
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