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
Show solution
Solution
Area = length × width = 30 × 20 = 600 m².
Correct Answer:
A
— 600 m²
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Volume of a rectangular prism = length × width × height = 3 × 4 × 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
Learn More →
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
Show solution
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
Learn More →
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
Learn More →
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
Learn More →
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
Show solution
Solution
Area of a rhombus = (1/2) × d1 × d2. Thus, Area = (1/2) × 12 × 16 = 96 cm².
Correct Answer:
A
— 96 cm²
Learn More →
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
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
Learn More →
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
Show solution
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
Learn More →
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
Learn More →
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
Learn More →
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
Show solution
Solution
Surface area of a sphere = 4πr² = 4π(7)² = 4π(49) = 196 cm².
Correct Answer:
B
— 196 cm²
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Area = (1/2) * (base1 + base2) * height = (1/2) * (10 + 6) * 4 = 32 cm².
Correct Answer:
A
— 32 cm²
Learn More →
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
Learn More →
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
Show solution
Solution
Area = (1/2) × base × height = (1/2) × 12 × 5 = 30 cm².
Correct Answer:
A
— 30 cm²
Learn More →
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
Learn More →
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
Learn More →
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
Learn More →
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
Learn More →
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
Learn More →
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)
Show solution
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)
Learn More →
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
Learn More →
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.
Show solution
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.
Learn More →
Q. If a line has the equation 2x - 3y + 6 = 0, what is the y-intercept of the line?
Show solution
Solution
To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, thus y = 2.
Correct Answer:
B
— 2
Learn More →
Q. If a line has the equation 3x - 4y + 12 = 0, what is its y-intercept?
Show solution
Solution
To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.
Correct Answer:
A
— 3
Learn More →
Showing 31 to 60 of 376 (13 Pages)
Geometry & Mensuration MCQ & Objective Questions
Geometry & Mensuration are crucial topics in mathematics that play a significant role in various school and competitive exams. Mastering these concepts not only enhances your problem-solving skills but also boosts your confidence during exams. Practicing MCQs and objective questions helps you familiarize yourself with the exam pattern, making it easier to tackle important questions effectively.
What You Will Practise Here
Understanding basic geometric shapes and their properties
Calculating area and perimeter of various figures
Exploring volume and surface area of 3D shapes
Applying the Pythagorean theorem in problem-solving
Utilizing important formulas for quick calculations
Interpreting diagrams and visual representations
Solving real-life problems using mensuration concepts
Exam Relevance
Geometry & Mensuration are integral parts of the mathematics syllabus for CBSE, State Boards, NEET, and JEE. These topics frequently appear in the form of objective questions and MCQs, often focusing on the application of formulas and theorems. Students can expect questions that require both theoretical understanding and practical application, making it essential to practice regularly to excel in these exams.
Common Mistakes Students Make
Confusing the formulas for area and perimeter
Overlooking units of measurement in calculations
Misinterpreting diagrams, leading to incorrect answers
Neglecting to apply the Pythagorean theorem correctly
Failing to check for the conditions of geometric properties
FAQs
Question: What are the key formulas I should remember for Geometry & Mensuration?Answer: Important formulas include area and perimeter for 2D shapes, volume and surface area for 3D shapes, and the Pythagorean theorem for right-angled triangles.
Question: How can I improve my speed in solving Geometry & Mensuration MCQs?Answer: Regular practice of MCQs and timed quizzes can help improve your speed and accuracy in solving these types of questions.
Start solving practice MCQs today to strengthen your understanding of Geometry & Mensuration. With consistent effort, you can master these topics and achieve your desired scores in exams!
