Area (Sector)：練習問題

A circular board has an area of \( 462 \text{ cm}^2 \). A teacher draws a sector on it with a central angle of \( 60^\circ \). What is the area of this sector?

A pizza with a radius of \( 10 \text{ cm} \) is cut into 5 equal sectors. What is the area of 2 of these slices? (Take \( \pi = 3.14 \))

The figure shows a rectangle \( ABCD \) where \( AB = 14 \text{ cm} \) and \( BC = 7 \text{ cm} \). Two identical quarter-circles are drawn inside the rectangle with centers at \( A \) and \( B \), both having a radius of \( 7 \text{ cm} \). Find the area of the region in the rectangle not covered by the two quarter-circles. (Take \( \pi = \frac{22}{7} \))

A circular cake has an area of \( 360 \text{ cm}^2 \). If a slice is cut out as a sector with a central angle of \( 40^\circ \), what is the area of this slice of cake?

A circle is divided into 12 equal sectors. If the radius of the circle is \( 6 \text{ cm} \), what is the area of a region formed by 5 of these sectors?
(Take \( \pi = 3.14 \))

A circular wall clock has an area of \( 600 \text{ cm}^2 \). If a student identifies a sector on the clock with a central angle of \( 60^\circ \), what is the area of this sector?

A local charity sells circular stickers with a radius of \( 7 \text{ cm} \). One section of the sticker is a sector with a central angle of \( 60^\circ \) and is colored red, while the rest is blue. What is the area of the blue part of the sticker? (Take \( \pi = \frac{22}{7} \))

A large circular board is divided into several sectors for a game. The total area of the circular board is \( 240 \text{ cm}^2 \). If the board is divided such that the central angle of the 'Jackpot' sector is \( 60^\circ \) and the central angle of the 'Bonus' sector is \( 120^\circ \), what is the combined area of the 'Jackpot' and 'Bonus' sectors?

The diagram shows a circular garden with a radius of \(14\text{ m}\). A portion of the garden, in the shape of a sector with a central angle of \(90^\circ\), is used as a sandpit.

(a) Calculate the area of the sandpit.
(b) If a fence is placed only along the curved edge of the sandpit, how long is the fence?

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

A local park features a circular flowerbed with a radius of \( 14 \text{ m} \). The garden is divided into several sections. One section is a sector used for growing roses, and the angle at the centre of this sector is \( 90^\circ \).

(a) Calculate the area of the rose sector. (Take \( \pi = \frac{22}{7} \))
(b) If the rest of the circular flowerbed is used for grass, what is the area of the grass section?
(c) If a small circular fountain with a diameter of \( 4 \text{ m} \) is placed exactly at the centre of the flowerbed, what is the remaining area of the rose sector? (Assume the fountain is also divided proportionally, round your final answer to the nearest whole number.)