Area (Circles): Practice Questions

A circular coin has a radius of \(14\text{ mm}\). What is the area of one face of the coin?
(Take \(\pi = \frac{22}{7}\))

The circumference of a circular plate is \(132\text{ cm}\). Find its area.
(Take \(\pi = \frac{22}{7}\))

A cow is tied to a corner of a rectangular barn that measures \(10\text{ m}\) by \(6\text{ m}\). The rope is \(8\text{ m}\) long. What is the maximum area the cow can graze outside the barn?
(Take \(\pi = 3.14\))

A circle has a diameter of \(10\text{ m}\). Calculate its area.
(Take \(\pi = 3.14\))

A large pizza has a diameter of \(12\text{ inches}\). If it is cut into \(8\) equal slices, what is the area of one slice?
(Take \(\pi = 3.14\))

An annulus is formed by two concentric circles. The radius of the inner circle is \( 7 \text{ cm} \) and the width of the ring is \( 7 \text{ cm} \). Calculate the area of the shaded ring.
(Take \( \pi = \frac{22}{7} \))

A square cardboard has a side length of \(14\text{ cm}\). From this cardboard, a circle with the largest possible area is cut out. What is the area of the remaining cardboard that was not part of the circle? (Take \(\pi = \frac{22}{7}\))

A rectangular lawn measures \(20\text{ m}\) by \(14\text{ m}\). A circular fountain with a diameter of \(7\text{ m}\) is built in the middle of the lawn, and a semi-circular flower bed with a radius of \(3.5\text{ m}\) is built along one of the shorter edges of the rectangular lawn.

Find the area of the remaining lawn not covered by the fountain or the flower bed. (Take \(\pi = \frac{22}{7}\))

A large circular plaza has a radius of \(14\text{ m}\). The center of the plaza contains a circular water fountain with a radius of \(3.5\text{ m}\). Surrounding the fountain, there are three identical semi-circular flower beds whose diameters are placed along the radius of the large plaza starting from the fountain's edge to the outer edge of the plaza.

(a) Calculate the area of the fountain.
(b) Calculate the total area of the three identical semi-circular flower beds.
(c) Find the remaining area of the plaza that is not covered by the fountain or the flower beds.

(Take \(\pi = \frac{22}{7}\))

A rectangular metal plate measures \(40\text{ cm}\) by \(30\text{ cm}\). An artist cuts out a circular piece with a radius of \(10\text{ cm}\) from the center. From the remaining four corners of the rectangular plate, the artist also removes four identical quarter-circles, each with a radius of \(7\text{ cm}\).

(a) Find the total area of the four quarter-circles removed. (Take \(\pi = \frac{22}{7}\))
(b) Find the area of the metal plate that remains after all the circular parts have been cut out. (Take \(\pi = 3.14\) for any calculations involving the central circular piece.)