A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of the second square is :
A. 2 : 5
B. 5 : 2
C. 4 : 5
D. 5 : 4
Answer: Option B
Solution(By Examveda Team)
Let the radius of each of the circle and the semi-circle be r unitsDiagonal of the first square = 2r units
Let the side of the second be a units
Then,
$$\eqalign{ & {r^2} = {a^2} + {\left( {\frac{a}{2}} \right)^2} \cr & \Rightarrow {r^2} = \frac{{5{a^2}}}{4} \cr & \Rightarrow {a^2} = \frac{{4{r^2}}}{5} \cr} $$
∴ Ratio of the areas of the two squares :
$$\eqalign{ & = \frac{{\frac{1}{2} \times {{\left( {2r} \right)}^2}}}{{{a^2}}} \cr & = \frac{{2{r^2}}}{{\left( {\frac{{4{r^2}}}{5}} \right)}} = \frac{5}{2} \cr & = \frac{5}{2} \cr & = 5:2 \cr} $$
Related Questions on Area
A. 15360 m2
B. 153600 m2
C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
A. 16 cm
B. 18 cm
C. 24 cm
D. Data inadequate
E. None of these
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
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