Q. What is the area of a sector of a circle with a radius of 4 cm and an angle of 90 degrees? (2023)
A.
4π cm²
B.
2π cm²
C.
8π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr²; = (90/360) × π(4)² = 2π cm².
Correct Answer:
B
— 2π cm²
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Q. What is the area of a sector of a circle with a radius of 7 cm and an angle of 90 degrees? (2022)
A.
38.5 cm²
B.
12.25 cm²
C.
15.4 cm²
D.
25.5 cm²
Show solution
Solution
Area of sector = (θ/360) * πr² = (90/360) * π * 7² = 38.5 cm².
Correct Answer:
A
— 38.5 cm²
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Q. What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)
A.
25π cm²
B.
50π cm²
C.
100π cm²
D.
75π cm²
Show solution
Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. What is the area of a sector of a circle with radius 6 cm and a central angle of 90 degrees? (2023)
A.
9π cm²
B.
12π cm²
C.
18π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 6² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
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Q. What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
A.
9π cm²
B.
12π cm²
C.
18π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
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Q. What is the area of a square inscribed in a circle of radius 10 cm?
A.
100 cm²
B.
200 cm²
C.
150 cm²
D.
50 cm²
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Solution
The diagonal of the square is equal to the diameter of the circle, which is 20 cm. Side of the square = diagonal / √2 = 20 cm / √2 = 10√2 cm. Area = (10√2 cm)² = 200 cm².
Correct Answer:
B
— 200 cm²
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Q. What is the area of a square with a perimeter of 40 cm?
A.
100 cm²
B.
200 cm²
C.
150 cm²
D.
250 cm²
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Solution
Perimeter of a square = 4 × side, so side = perimeter / 4 = 40 cm / 4 = 10 cm. Area = side × side = 10 cm × 10 cm = 100 cm².
Correct Answer:
A
— 100 cm²
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Q. What is the area of a square with a side length of 8 cm? (2023)
A.
64 cm²
B.
32 cm²
C.
16 cm²
D.
48 cm²
Show solution
Solution
Area = side² = 8² = 64 cm²
Correct Answer:
A
— 64 cm²
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Q. What is the area of a trapezium with bases 10 cm and 6 cm, and height 4 cm?
A.
32 cm²
B.
40 cm²
C.
24 cm²
D.
28 cm²
Show solution
Solution
Area = 1/2 × (base1 + base2) × height = 1/2 × (10 cm + 6 cm) × 4 cm = 32 cm².
Correct Answer:
A
— 32 cm²
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Q. What is the area of a trapezium with bases 5 cm and 7 cm, and height 4 cm? (2023)
A.
24 cm²
B.
20 cm²
C.
30 cm²
D.
28 cm²
Show solution
Solution
Area = 1/2 * (base1 + base2) * height = 1/2 * (5 + 7) * 4 = 24 cm²
Correct Answer:
A
— 24 cm²
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Q. What is the area of a trapezium with bases of 10 cm and 6 cm, and a height of 4 cm?
A.
32 cm²
B.
40 cm²
C.
24 cm²
D.
28 cm²
Show solution
Solution
Area = 1/2 × (base1 + base2) × height = 1/2 × (10 cm + 6 cm) × 4 cm = 32 cm².
Correct Answer:
A
— 32 cm²
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Q. What is the area of a triangle formed by the points (0, 0), (4, 0), and (0, 3)?
Show solution
Solution
The area of a triangle is given by (1/2) * base * height. Here, base = 4 and height = 3, so area = (1/2) * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. What is the area of a triangle with a base of 10 cm and a height of 5 cm?
A.
25 cm²
B.
50 cm²
C.
15 cm²
D.
30 cm²
Show solution
Solution
The area of a triangle is given by the formula (1/2) * base * height. Thus, Area = (1/2) * 10 * 5 = 25 cm².
Correct Answer:
A
— 25 cm²
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Q. What is the area of a triangle with a base of 10 units and a height of 5 units?
A.
25 square units
B.
50 square units
C.
15 square units
D.
30 square units
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 square units.
Correct Answer:
A
— 25 square units
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Q. What is the area of a triangle with a base of 12 cm and a height of 5 cm? (2022)
A.
30 cm²
B.
60 cm²
C.
24 cm²
D.
36 cm²
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 12 * 5 = 30 cm².
Correct Answer:
A
— 30 cm²
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Q. What is the area of a triangle with a base of 6 cm and a height of 4 cm?
A.
12 cm²
B.
24 cm²
C.
18 cm²
D.
30 cm²
Show solution
Solution
Area = 1/2 × base × height = 1/2 × 6 cm × 4 cm = 12 cm².
Correct Answer:
A
— 12 cm²
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Q. What is the area of a triangle with a base of 8 cm and a height of 5 cm? (2020)
A.
20 cm²
B.
30 cm²
C.
40 cm²
D.
10 cm²
Show solution
Solution
The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².
Correct Answer:
A
— 20 cm²
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Q. What is the area of a triangle with base 10 and height 5?
Show solution
Solution
Area = (1/2) * base * height = (1/2) * 10 * 5 = 25.
Correct Answer:
A
— 25
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Q. What is the area of a triangle with base 10 cm and height 5 cm? (2021)
A.
25 cm²
B.
50 cm²
C.
15 cm²
D.
30 cm²
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 cm².
Correct Answer:
A
— 25 cm²
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Q. What is the area of a triangle with vertices at (0,0), (4,0), and (0,3)?
Show solution
Solution
The area is calculated as (1/2) * base * height = (1/2) * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. What is the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0)? (2022)
Show solution
Solution
Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.
Correct Answer:
A
— 0.5
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Q. What is the area of an ellipse with semi-major axis 7 and semi-minor axis 4?
A.
28π
B.
14π
C.
21π
D.
35π
Show solution
Solution
The area of an ellipse is given by A = πab. Here, A = π * 7 * 4 = 28π.
Correct Answer:
A
— 28π
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Q. What is the area of an equilateral triangle with a side length of 6 cm? (2022)
A.
9√3 cm²
B.
12√3 cm²
C.
18√3 cm²
D.
24√3 cm²
Show solution
Solution
Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².
Correct Answer:
A
— 9√3 cm²
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Q. What is the area of an equilateral triangle with side length 'a'?
A.
(√3/4)a²
B.
(1/2)a²
C.
(√2/2)a²
D.
(3/2)a²
Show solution
Solution
The area of an equilateral triangle is given by the formula (√3/4)a².
Correct Answer:
A
— (√3/4)a²
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Q. What is the area of the base of a cone with radius 3? (2023)
Show solution
Solution
Area of base = πr² = π(3²) = 9π square units.
Correct Answer:
A
— 9π
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Q. What is the area of the base of a cylinder with radius 4 units? (2020)
A.
16π
B.
8π
C.
12π
D.
20π
Show solution
Solution
Area of base = πr² = π(4)² = 16π square units.
Correct Answer:
A
— 16π
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Q. What is the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3)?
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. What is the area under the curve y = 1/x from x = 1 to x = 2?
A.
ln(2)
B.
1
C.
ln(2) - 1
D.
0
Show solution
Solution
The area is given by the integral from 1 to 2 of 1/x dx. This evaluates to [ln(x)] from 1 to 2 = ln(2) - ln(1) = ln(2).
Correct Answer:
A
— ln(2)
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Q. What is the area under the curve y = 1/x from x = 1 to x = 4?
A.
ln(4)
B.
ln(3)
C.
ln(2)
D.
ln(1)
Show solution
Solution
The area under the curve is given by ∫(from 1 to 4) (1/x) dx = [ln(x)] from 1 to 4 = ln(4) - ln(1) = ln(4).
Correct Answer:
A
— ln(4)
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Q. What is the area under the curve y = 2x^2 + 3 from x = 0 to x = 2?
Show solution
Solution
The area under the curve is given by ∫(from 0 to 2) (2x^2 + 3) dx = [(2/3)x^3 + 3x] from 0 to 2 = (16/3 + 6) = 10.
Correct Answer:
B
— 12
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