Question

Each of the congruent circles shown is externally tangent to other circles and/or to the side(s) of the rectangles as shown. If each circle has circumference $16\pi$, then the length of a diagonal of the rectangle is

• A. $80$
• B. $40$
• C. $20$
• D. $15$

Answer 1

The correct option is A $80$

Circumference
of the circle $=2\pi r=16\pi$
$=>r=8$
Diameter of each circle $=16$
As there are 4 circles along the length and 3 along the breadth,
Length of the rectangle $=16\times 4=64$
Breadth $=16\times 3=48$
Diagonal of the rectangle $=\sqrt{{length}^2+{breadth}^2}=\sqrt{{64}^2+{48}^2}=\sqrt{6400}=80$