What is the <strong>MAXIMUM</strong> area that can be covered by three non-intersecting circles drawn inside a rectangle of sides 8 cm and 12 cm?

Explanation

To maximize the area, fit one largest possible circle and two smaller ones. The largest circle has a diameter of 8 cm (radius 4 cm), taking up an 8 \times 8 section. Area = \pi(4^2) = 16\pi. In the remaining 4 \times 8 area, we can fit two circles of diameter 4 cm (radius 2 cm) side by side. Their combined area is 2 \times \pi(2^2) = 8\pi. Total maximum area = 16\pi + 8\pi = 24\pi square cm.

Related questions on Mensuration

• A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
• A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
• A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
• A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
• Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...