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If the radius of a circle is increased by 200%, then its area will increase by :
Answer & Solution
Correct Answer:
Option
C
Let the original radius be R
New radius = (100 + 200)% of R = 300% of R = 3R
Original area = $$\pi $$R2
New area = $$\pi $$ × (3R)2 = 9$$\pi $$R2
Increase in area :
$$\eqalign{ & = \left( {9\pi {{\text{R}}^2} - \pi {{\text{R}}^2}} \right) \cr & = 8\pi {{\text{R}}^2} \cr} $$
∴ Increase %:
$$\eqalign{ & = \left( {\frac{{8\pi {{\text{R}}^2}}}{{\pi {{\text{R}}^2}}} \times 100} \right)\% \cr & = 800\% \cr} $$
New radius = (100 + 200)% of R = 300% of R = 3R
Original area = $$\pi $$R2
New area = $$\pi $$ × (3R)2 = 9$$\pi $$R2
Increase in area :
$$\eqalign{ & = \left( {9\pi {{\text{R}}^2} - \pi {{\text{R}}^2}} \right) \cr & = 8\pi {{\text{R}}^2} \cr} $$
∴ Increase %:
$$\eqalign{ & = \left( {\frac{{8\pi {{\text{R}}^2}}}{{\pi {{\text{R}}^2}}} \times 100} \right)\% \cr & = 800\% \cr} $$
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