Question : The hour hand moves through 4 hours and has a length of 6 cm. Find the area (in cm2, rounded off to two decimal places) of the sector covered by the hour hand.
Option 1: 32.69
Option 2: 30.67
Option 3: 37.71
Option 4: 35.75
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Correct Answer: 37.71
Solution : In 4 hours, the hour hand covers = $0.5° \times 4 \times 60 = 120°$ Now, the area of the sector covered by the hour hand = $\pi \times 6^2\times \frac{120°}{360°}$ ⇒ Area = $12\pi = 37.71\ \mathrm{cm^2}$ Hence, the correct answer is 37.71.
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Question : Find the area of the sector of a circle with a radius of 5 cm and an angle of 60° (rounded off to one decimal).
Option 1: 12.8 cm2
Option 2: 14.1 cm2
Option 3: 13.1 cm2
Option 4: 15.1 cm2
Question : The area of a sector of a circle of radius 28 cm is 112 cm2. Find the length of the corresponding arc of the sector.
Option 1: 4 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 5 cm
Question : If the side of an equilateral triangle is 8 cm, then find the area of the triangle (correct to two decimal places).
Option 1: 27.17 cm2
Option 2: 27.27 cm2
Option 3: 27.71 cm2
Option 4: 27.72 cm2
Question : The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the surface area of the pipe (take $\pi=\frac{22}{7}$ ) correct to two places of decimal.
Option 1: 1,662.67 cm2
Option 2: 1,552.57 cm2
Option 3: 1,442.48 cm2
Option 4: 1,772.76 cm2
Question : The curved surface area of the sphere is 154 cm2. Find the volume of the sphere (rounded off to one digit after decimal).
Option 1: 156.9 cm3
Option 2: 179.7 cm3
Option 3: 161.1 cm3
Option 4: 147.8 cm3
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