Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circles. If the remaining area of the square is $168 \mathrm{cm}^{2}$, what is the size of the radius of the circle?(in centimeters) [RBI Officers Gr. 'B' (Phase I) Exam, 2015]
(a)14
(b)1.4
(c)35
(d)21
Answer
Answer (as printed): A
Explanation
Let the radius of each circle be ' $r^{\prime}$ cm. Then the side of the square will be ' $2 r^{\prime}$ cm Area covered by the four circles in the square $$=4 \times \frac{1}{4} \times \pi r^{2}=\pi r^{2} \mathrm{cm}^{2}$$ Area of the square $=(2 r)^{2}=4 r^{2} \mathrm{cm}^{2}$ Now, according to the question, Remaining area of the square $$\begin{aligned} & 4 r^{2}-\pi r^{2}=168 \\ & r^{2}\left(4-\frac{22}{7}\right)=168 \\ & r^{2} \times(28-22)=168 \times 7 \\ & r^{2}=\frac{168 \times 7}{6}=28 \times 7=7 \times 4 \times 7 \\ & \therefore r=\sqrt{7 \times 7 \times 4}=7 \times 2=14 \mathrm{cm} . \end{aligned}$$