Q. A rectangular garden has a length of 30 meters and a width of 20 meters. What is the area of the garden?
A.
600 m²
B.
500 m²
C.
400 m²
D.
300 m²
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Solution
Area = length × width = 30 × 20 = 600 m².
Correct Answer:
A
— 600 m²
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Q. A rectangular garden is 10 m long and 6 m wide. If a path of width 1 m is built around it, what is the area of the path? (2023)
A.
32 m²
B.
36 m²
C.
40 m²
D.
44 m²
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Solution
Area of the garden = 10 * 6 = 60 m². Area including the path = (10 + 2) * (6 + 2) = 12 * 8 = 96 m². Area of the path = 96 - 60 = 36 m².
Correct Answer:
B
— 36 m²
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Q. A rectangular garden is 30 meters long and 20 meters wide. If a path of 1 meter width is built around it, what is the area of the path?
A.
80 m²
B.
100 m²
C.
120 m²
D.
140 m²
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Solution
Area of the garden = 30 × 20 = 600 m². Area including the path = (30 + 2) × (20 + 2) = 32 × 22 = 704 m². Area of the path = 704 - 600 = 104 m².
Correct Answer:
B
— 100 m²
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Q. A rectangular plot has a length of 50 meters and a width of 30 meters. If a path of 2 meters width is built around it, what is the area of the path?
A.
320 m²
B.
400 m²
C.
600 m²
D.
800 m²
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Solution
Total area with path = (50 + 4) × (30 + 4) = 54 × 34 = 1836 m². Area of the plot = 50 × 30 = 1500 m². Area of the path = 1836 - 1500 = 336 m².
Correct Answer:
B
— 400 m²
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Q. A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. What is its volume?
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
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Solution
Volume of a rectangular prism = length × width × height = 3 × 4 × 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
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Q. A rectangular prism has dimensions 3 m, 4 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
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Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(3*4 + 3*5 + 4*5) = 2(12 + 15 + 20) = 2(47) = 94 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular prism has dimensions 4 m, 3 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*3 + 4*5 + 3*5) = 2(12 + 20 + 15) = 2(47) = 94 m².
Correct Answer:
B
— 60 m²
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Q. A rectangular prism has dimensions 4 m, 5 m, and 6 m. What is its surface area?
A.
94 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*5 + 4*6 + 5*6) = 94 m².
Correct Answer:
A
— 94 m²
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Q. A rhombus has diagonals of lengths 12 cm and 16 cm. What is the area of the rhombus?
A.
96 cm²
B.
48 cm²
C.
72 cm²
D.
60 cm²
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Solution
Area of a rhombus = (1/2) × d1 × d2. Thus, Area = (1/2) × 12 × 16 = 96 cm².
Correct Answer:
A
— 96 cm²
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Q. A semicircle has a diameter of 14 cm. What is its area? (Use π ≈ 3.14)
A.
76.96 cm²
B.
48.96 cm²
C.
38.48 cm²
D.
28.96 cm²
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Solution
Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = 76.96 cm².
Correct Answer:
A
— 76.96 cm²
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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle?
A.
49 cm²
B.
77 cm²
C.
154 cm²
D.
100 cm²
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Solution
Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = (1/2) × 3.14 × 49 = 76.96 cm², which rounds to 77 cm².
Correct Answer:
B
— 77 cm²
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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 22/7)
A.
77 cm²
B.
49 cm²
C.
154 cm²
D.
88 cm²
Show solution
Solution
Radius = 7 cm. Area of semicircle = (1/2) × πr² = (1/2) × (22/7) × (7)² = 77 cm².
Correct Answer:
A
— 77 cm²
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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 3.14)
A.
76.96 cm²
B.
48.96 cm²
C.
38.48 cm²
D.
24.48 cm²
Show solution
Solution
Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = 76.96 cm².
Correct Answer:
A
— 76.96 cm²
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Q. A sphere has a radius of 7 cm. What is its surface area?
A.
154 cm²
B.
196 cm²
C.
308 cm²
D.
616 cm²
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Solution
Surface area of a sphere = 4πr² = 4π(7)² = 4π(49) = 196 cm².
Correct Answer:
B
— 196 cm²
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Q. A square has a perimeter of 40 cm. What is the area of the square?
A.
100 cm²
B.
200 cm²
C.
150 cm²
D.
250 cm²
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Solution
Perimeter of a square = 4 × side. Thus, 40 = 4 × side, giving side = 10 cm. Area = side² = 10² = 100 cm².
Correct Answer:
A
— 100 cm²
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Q. A square has a perimeter of 48 cm. What is the area of the square?
A.
144 cm²
B.
64 cm²
C.
36 cm²
D.
100 cm²
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Solution
Perimeter of a square = 4 × side. Thus, 48 = 4 × side, giving side = 12 cm. Area = side² = 12² = 144 cm².
Correct Answer:
A
— 144 cm²
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Q. A square has a perimeter of 64 cm. What is the length of one side of the square?
A.
16 cm
B.
12 cm
C.
14 cm
D.
8 cm
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Solution
The perimeter of a square is given by P = 4s, where s is the length of one side. Therefore, 4s = 64 cm, leading to s = 16 cm.
Correct Answer:
A
— 16 cm
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Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is its area? (2023)
A.
32 cm²
B.
36 cm²
C.
40 cm²
D.
44 cm²
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Solution
Area = (1/2) * (base1 + base2) * height = (1/2) * (10 + 6) * 4 = 32 cm².
Correct Answer:
A
— 32 cm²
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Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is the area of the trapezium?
A.
32 cm²
B.
40 cm²
C.
36 cm²
D.
28 cm²
Show solution
Solution
Area of a trapezium = (1/2) × (base1 + base2) × height = (1/2) × (10 + 6) × 4 = 32 cm².
Correct Answer:
A
— 32 cm²
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Q. A triangle has a base of 12 cm and a height of 5 cm. What is the area of the triangle?
A.
30 cm²
B.
60 cm²
C.
24 cm²
D.
12 cm²
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Solution
Area = (1/2) × base × height = (1/2) × 12 × 5 = 30 cm².
Correct Answer:
A
— 30 cm²
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Q. A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the triangle?
A.
24 cm²
B.
30 cm²
C.
36 cm²
D.
20 cm²
Show solution
Solution
Using Heron's formula, s = (6 + 8 + 10)/2 = 12. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12 × 6 × 4 × 2] = 24 cm².
Correct Answer:
A
— 24 cm²
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Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
168 cm²
Show solution
Solution
The triangle is a right triangle (7² + 24² = 25²). The area is (1/2) * base * height = (1/2) * 7 * 24 = 84 cm².
Correct Answer:
A
— 84 cm²
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Q. If a circle has a circumference of 62.8 cm, what is its diameter?
A.
10 cm
B.
20 cm
C.
30 cm
D.
40 cm
Show solution
Solution
Using the formula C = πd, we find d = C/π = 62.8/3.14 = 20 cm.
Correct Answer:
B
— 20 cm
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Q. If a circle has a radius of 10 cm, what is the length of an arc that subtends a central angle of 90 degrees?
A.
15.7 cm
B.
25 cm
C.
17.5 cm
D.
20 cm
Show solution
Solution
The length of an arc is given by L = (θ/360) * 2πr. Here, L = (90/360) * 2π(10) = 17.5 cm.
Correct Answer:
C
— 17.5 cm
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Q. If a circle has a radius of 7 cm, what is its area? (2020)
A.
154 cm²
B.
49 cm²
C.
28 cm²
D.
14 cm²
Show solution
Solution
The area of a circle is calculated using A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
Correct Answer:
A
— 154 cm²
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Q. If a circle is centered at (0, 0) with a radius of 5, which of the following points lies outside the circle?
A.
(3, 4)
B.
(0, 5)
C.
(5, 0)
D.
(6, 0)
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Solution
The equation of the circle is x² + y² = 25. The point (6, 0) gives 6² + 0² = 36, which is greater than 25, hence it lies outside.
Correct Answer:
D
— (6, 0)
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Q. If a cube has a volume of 64 cubic centimeters, what is the length of one side of the cube?
A.
4 cm
B.
8 cm
C.
16 cm
D.
2 cm
Show solution
Solution
Volume of a cube = side³. Therefore, side = ∛64 = 4 cm.
Correct Answer:
A
— 4 cm
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Q. If a hexagon is regular, what is the relationship between its sides and angles?
A.
All sides are equal, and all angles are equal.
B.
Sides can be of different lengths, but angles are equal.
C.
Sides are equal, but angles can vary.
D.
No specific relationship exists.
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Solution
In a regular hexagon, all sides are equal in length and all interior angles are equal.
Correct Answer:
A
— All sides are equal, and all angles are equal.
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Q. If a line has the equation 2x - 3y + 6 = 0, what is the y-intercept of the line?
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Solution
To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, thus y = 2.
Correct Answer:
B
— 2
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Q. If a line has the equation 3x - 4y + 12 = 0, what is its y-intercept?
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Solution
To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.
Correct Answer:
A
— 3
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