Q. If the area of a circle is 154 cm², what is the radius of the circle? (Use π = 22/7)
A.
7 cm
B.
14 cm
C.
21 cm
D.
28 cm
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Solution
Area = πr². 154 = (22/7)r². Solving gives r² = 154 * 7 / 22 = 49, so r = 7 cm.
Correct Answer: A — 7 cm
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Q. If the area of a circle is 36π, what is the radius?
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Solution
Area = πr^2 => 36π = πr^2 => r^2 = 36 => r = 6.
Correct Answer: A — 6
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Q. If the area of a circle is 50π, what is the radius?
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Solution
Area = πr^2 => 50π = πr^2 => r^2 = 50 => r = √50 = 5√2.
Correct Answer: B — 10
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Q. If the area of a circle is 78.5 cm², what is the radius? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
6 cm
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Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.
Correct Answer: B — 7 cm
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Q. If the area of a coil is doubled while keeping the magnetic field constant, what happens to the magnetic flux through the coil? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Magnetic flux (Φ) is given by the product of magnetic field (B) and area (A). If the area is doubled and the magnetic field remains constant, the magnetic flux also doubles.
Correct Answer: A — It doubles
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Q. If the area of a loop in a magnetic field is doubled while keeping the magnetic field strength constant, what happens to the magnetic flux through the loop?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled and the magnetic field (B) remains constant, the magnetic flux also doubles.
Correct Answer: A — It doubles
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Q. If the area of a loop in a magnetic field is doubled while keeping the magnetic field strength constant, what happens to the magnetic flux?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled, the magnetic flux also doubles.
Correct Answer: A — It doubles
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Q. If the area of a loop is doubled while keeping the magnetic field constant, how does the magnetic flux change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It halves
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Solution
Magnetic flux Φ is given by Φ = B * A. If the area A is doubled while B remains constant, the magnetic flux also doubles.
Correct Answer: B — It doubles
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Q. If the area of a loop is doubled while the magnetic field remains constant, how does the induced EMF change?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Induced EMF is proportional to the area of the loop. If the area is doubled, the induced EMF also doubles.
Correct Answer: A — Doubles
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Q. If the area of a parallelogram is 120 square units and the base is 15 units, what is the height?
A.
8 units
B.
10 units
C.
12 units
D.
15 units
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Solution
Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 units.
Correct Answer: B — 10 units
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Q. If the area of a parallelogram is given by the formula base times height, what happens to the area if the height is halved?
A.
The area remains the same
B.
The area doubles
C.
The area is halved
D.
The area increases by 25%
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Solution
If the height of a parallelogram is halved, the area is also halved, as area = base × height.
Correct Answer: C — The area is halved
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Q. If the area of a quadrilateral is given by the formula A = 1/2 * d1 * d2 * sin(θ), where d1 and d2 are the lengths of the diagonals and θ is the angle between them, which type of quadrilateral does this formula apply to?
A.
Rectangle
B.
Parallelogram
C.
Kite
D.
Trapezium
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Solution
This formula applies to a kite, where the diagonals intersect at an angle.
Correct Answer: C — Kite
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Q. If the area of a quadrilateral is given by the formula A = 1/2 * d1 * d2 * sin(θ), what do d1 and d2 represent? (2023)
A.
The lengths of the sides.
B.
The lengths of the diagonals.
C.
The lengths of the altitudes.
D.
The lengths of the bases.
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Solution
In the formula for the area of a quadrilateral, d1 and d2 represent the lengths of the diagonals.
Correct Answer: B — The lengths of the diagonals.
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Q. If the area of a rectangle is 48 square meters and the length is 8 meters, what is the width?
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Solution
Area = Length * Width. Therefore, Width = Area / Length = 48 / 8 = 6 meters.
Correct Answer: B — 6
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Q. If the area of a rectangle is 48 square units and the length is 8 units, what is the width? (2022)
A.
4 units
B.
6 units
C.
8 units
D.
10 units
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Solution
Area = Length × Width. Therefore, Width = Area / Length = 48 / 8 = 6 units.
Correct Answer: A — 4 units
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Q. If the area of a rectangle is calculated as 30 m² with an uncertainty of ±0.5 m², what is the relative error in the area measurement?
A.
0.0167
B.
0.017
C.
0.015
D.
0.02
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Solution
Relative error = (absolute error / measured value) = 0.5 / 30 = 0.0167.
Correct Answer: A — 0.0167
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Q. If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?
A.
1 m²
B.
0.5 m²
C.
0.2 m²
D.
0.1 m²
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Solution
Uncertainty in area = 2 * length * uncertainty in length = 2 * 10 * 0.1 = 2 m².
Correct Answer: B — 0.5 m²
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Q. If the area of a sector of a circle is 25π cm² and the radius is 10 cm, what is the angle of the sector in degrees?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
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Solution
Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(10)². Solving gives θ = 90 degrees.
Correct Answer: A — 90 degrees
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Q. If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?
A.
90°
B.
60°
C.
45°
D.
30°
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Solution
Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(5)². Solving gives θ = 90°.
Correct Answer: A — 90°
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Q. If the area of a sector of a circle is 30 cm² and the radius is 5 cm, what is the angle of the sector in degrees?
A.
60°
B.
72°
C.
90°
D.
120°
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Solution
Area of a sector = (θ/360) × πr². Thus, 30 = (θ/360) × π × 25. Solving gives θ = (30 × 360)/(25π) ≈ 72°.
Correct Answer: B — 72°
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Q. If the area of a square is 64 cm², what is the length of one side? (2022)
A.
6 cm
B.
7 cm
C.
8 cm
D.
9 cm
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Solution
Area of a square = side². Therefore, side = √64 = 8 cm.
Correct Answer: C — 8 cm
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Q. If the area of a trapezium is 60 square units and the lengths of the parallel sides are 10 units and 20 units, what is the height?
A.
4 units
B.
6 units
C.
8 units
D.
10 units
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Solution
Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.
Correct Answer: B — 6 units
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Q. If the area of a trapezium is 60 square units and the lengths of the two parallel sides are 10 units and 20 units, what is the height?
A.
4 units
B.
6 units
C.
5 units
D.
8 units
Show solution
Solution
Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.
Correct Answer: B — 6 units
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Q. If the area of a triangle is 24 cm² and the base is 8 cm, what is the height?
A.
6 cm
B.
8 cm
C.
12 cm
D.
3 cm
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Solution
Area = 1/2 * base * height. Therefore, 24 = 1/2 * 8 * height, which gives height = 6 cm.
Correct Answer: A — 6 cm
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Q. If the area of a triangle is 24 square cm and the base is 8 cm, what is the height?
A.
3 cm
B.
6 cm
C.
8 cm
D.
12 cm
Show solution
Solution
The area of a triangle is given by the formula Area = 1/2 * base * height. Thus, 24 = 1/2 * 8 * height, which gives height = 6 cm.
Correct Answer: B — 6 cm
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Q. If the area of a triangle is 30 cm² and the base is 10 cm, what is the height? (2020)
A.
3 cm
B.
6 cm
C.
9 cm
D.
12 cm
Show solution
Solution
Area = 1/2 * base * height. Thus, 30 = 1/2 * 10 * height. Solving gives height = 6 cm.
Correct Answer: B — 6 cm
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Q. If the area of a triangle is 30 square units and the base is 10 units, what is the height?
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Solution
Area = 1/2 * base * height => height = 30/(1/2 * 10) = 6.
Correct Answer: B — 5
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Q. If the area of a triangle is 48 cm² and the base is 12 cm, what is the height? (2022)
A.
6 cm
B.
8 cm
C.
4 cm
D.
10 cm
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Solution
Area = 1/2 * base * height, so 48 = 1/2 * 12 * height, height = 48/(6) = 8 cm.
Correct Answer: B — 8 cm
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Q. If the area of a triangle is 50 square units and its base is 10 units, what is the height of the triangle?
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
Solution
Area of a triangle = (1/2) × base × height. Thus, 50 = (1/2) × 10 × height. Solving gives height = 10 units.
Correct Answer: A — 5 units
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Q. If the area of a triangle is 60 square units and the base is 10 units, what is the height? (2019)
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Solution
The area of a triangle is given by (1/2) * base * height. Thus, 60 = (1/2) * 10 * height. Solving for height gives height = 12 units.
Correct Answer: A — 12
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