Sector, segment, combined figures MCQs

Q1. A sector-shaped flag is cut so that its two straight edges and curved edge together measure 53 cm of trim, with each straight edge 21 cm. What area of cloth is in the flag?

• A.115.5 cm^2
• B.556.5 cm^2
• C.11 cm
• D.1386 cm^2

Answer: A. 115.5 cm^2

Perimeter = 2r + arc, so arc = 53 - 2*21 = 11 cm. Sector area = (1/2)*arc*r = (1/2)*11*21 = 115.5 cm^2.

Q2. A triangular sail is cut as large as possible from a semicircular sheet of canvas of radius 10 m, with its base along the straight edge. What is the maximum area of the sail?

• A.50 m^2
• B.200 m^2
• C.100 m^2
• D.157.1429 m^2

Answer: C. 100 m^2

The largest triangle in a semicircle has the diameter as base (2r) and the apex on the arc giving height r. Area = (1/2)*base*height = (1/2)*(2*10)*10 = 100 m^2.

Q3. Two concentric ripples on a pond have radii in the ratio 2 : 5. In what ratio do the areas they enclose stand?

• A.2 : 5
• B.4 : 10
• C.4 : 25
• D.8 : 125

Answer: C. 4 : 25

Area scales as radius^2, so the area ratio = 2^2 : 5^2 = 4 : 25.