Area of cut out regular Surfaces and Irregular surfaces

Workshop Calculation and Science, Module-2

Posted May 14, 2025

By Roni

6 min read

Area of cut out regular Surfaces and Irregular surfaces

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Q1: Which formula is suitable for the area of a circle whose diameter is (d)?

\(\frac{\pi d^2}{4}\)
\(\pi r\)
\(2\pi r\)
\(\pi d\)

Q2: What is the circumference of a semi circle?

\(\pi r + 2r\)
\(4\pi d\)
\(2\pi r^2\)
\(4\pi d^2\)

Q3: What is the area of irregular shape by Simpson's rule?

\(\frac{3h}{8} \left[y_1 + y_n + 4(y_2 + y_4 + y_6) + 2(y_3 + y_5)\right]\)
\(2h [y_1 + y_n]\)
\(3h [y_2 + y_4 + y_6]\)
\(2h [y_1 + y_n + (y_2 + y_3)]\)

Q4: What is the name called biggest chord of the circle?

Arc
Diameter
Radius
Diagonal

Q5: What is the formula for circumference of a circle?

\(\pi r^2\)
\(4\pi d^2\)
\(2 \pi r\)
\(2 \pi r^2\)

Q6: What is the formula for area of the semi circle?

\(\pi r^2\)
\(2 \pi r\)
\(\pi r\)
\(\frac{\pi r^2}{2}\)

Q7: What is the formula for area of the circle?

\(2\pi r^2\)
\(\pi r^2\)
\(2 \pi r\)
\(2 \pi d\)

Q8: What is the area of the irregular surface?

1400 mm²
1450 mm²
1500 mm²
1200 mm²

Q9: What is the area of the shaded portion, Equilateral Triangle side is 6cm and circle radius is 1.5cm?

8.52 cm²
12.75 cm³
9.5 cm³
12.25 cm²

Q10: What is the area of the irregular surfaces?

2500 mm²
3544 mm²
3250 mm²
3444 mm²

Q11: What is the area of the irregular surfaces?

4800 mm²
4820 mm²
4830 mm²
4843 mm²

Q12: What is the area of irregular surfaces?

1350 mm²
1175 mm²
1150 mm²
1250 mm²

Q13: What is the length of arc of a sector, whose perimeter is 64.8cm and radius is 12.4 cm?

40 cm
45 cm
40.8 cm
42 cm

Q14: What is the length of arc of the sector whose radius is 15 cm and the intended angle is 30°?

7.85 cm
7.25 cm
6.75 cm
6.85 cm

Q15: What is the area of the sector, if the diameter is 12 cm and the angle is 60°?

18.0 cm²
17.75 cm²
19.00 cm²
18.84 cm²

Q16: What is the formula for area of the segment of a circle?

Area of the sector - Area of the triangle
Area of the circle
Area of the sector
Area of the triangle Area of the sector

Q17: What is the area of the circle, if the circumference of the circle is 44 cm?

128 cm²
130 cm²
154 cm²
129 cm²

Q18: What is the area of the irregular surfaces?

2600 unit²
2590 unit²
2625 unit²
2620 unit²

Q19: What is the area of the irregular surfaces?

4200 unit²
4300 unit²
4500 unit²
4400 unit²

Q20: What is the radius of the circle if the angle of sector is 90° and the area of the circle is 196 cm²?

15.77 cm
15 cm
14.85 cm
14.95 cm

Q21: What is the formula for perimeter of a sector?

2l + r
l + 2r
πr²
2πr

Q22: What is the area of conical object?

5100 mm²
5120 mm²
5125 mm²
5158.8 mm²

Q23: What is the area of the lamina?

14,800 mm²
14,600 mm²
14,650 mm²
14,750 mm²

Q24: What is the area of the sector, whose diameter is 40 mm and angle is 120°?

418.66 mm²
400.50 mm²
415.5 mm²
416.6 mm²

Q25: What is the length of arc of a sector, whose radius is 15 cm and angle is 40°?

9.75 cm
9.8 cm
10.60 cm
10.4 cm

Q26: What is the length of arc of a sector whose radius is 3.6 cm and angle is 36°?

2.10 cm
2.26 cm
22.6 cm
2.36 cm

Q27: What is the area of the surface?

Q28: What is the name of the shaded portion?

<ul> <li onclick="checkAnswer(this, true)" data-correct="true">Segment</li> <li onclick="checkAnswer(this, false)" data-correct="false">Sector</li> <li onclick="checkAnswer(this, false)" data-correct="false">Arc</li> <li onclick="checkAnswer(this, false)" data-correct="false">Chord</li> </ul> <hr>

Q29: Which line is called as chord?

Q30: What is the area of the circle, whose diameter is 50 cm?

1900 cm²
1950 cm²
1962.5 cm²
1960 cm²

Q31: What is the name of the region of a circle between any two point on the circumference?

Arc
Segment
Sector
Chord

Q32: What is the radius of the circle, whose circumference is 440 cm?

71.5 cm
70 cm
70.5 cm
72.2 cm

Q33: What is the area of a circular surface if the radius is 14 cm?

615.44 cm²
614.5 cm²
612.25 cm²
612.44 cm²

Q34: What is the circumference of a circle whose diameter is 7 cm?

22 cm
44 cm
25 cm
21 cm

Q35: What is the radius of a circle whose diameter is 44 cm?

44 cm
22 cm
23 cm
20 cm

Q36: What is the diameter of the circle, if the area of the circle is 78.5 cm² ?

5 cm
10 cm
15 cm
5.5 cm

Q37: What is the area of the circle if the radius is 10cm?

314 cm²
31.4 cm²
30.4 cm²
3.14 cm²

Q38: What is the radius of the semicircle, if the circumference of the semicirle is 28.26 cm?

5.49 cm
6.49 cm
8.5 cm
8.75 cm

Q39: What is the diameter of the semicircle, if the circumference of the semicircle is 21.98 cm?

8.55 cm
8 cm
7.55 cm
7 cm

Q40: What is the area of the semicircle, if the diameter is 14 cm?

70 cm²
76.93 cm²
75.06 cm²
86.93 cm²

Q41: What is the diameter of the circle, if the area of the circle is 706.5 cm² ?

29 cm
29.5 cm
30 cm
30.5 cm

Q42: What is the diameter of the circle, if the circumference is 31.4 cm?

5 cm
10 cm
8 cm
8.5 cm

Q43: What is the area of the lamina?

Q44: What is the area of the irregular lamina?

Q45: What is the area of the lamina?

Q46: What is the area of irregular surfaces?

Q47: What is the area of shaded portion whose OD = 38 mm. ID = 32 mm?

Q48: What is the area of irregular surfaces whose equilateral triangle size is 20 mm?

Q49: What is the area of shaded portion. Whose square size 300mm?

Q50: What is the area of shaded portion?

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2nd year, WCS

WCS ITI

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