Mensuration MCQ & Objective Questions
Mensuration is a crucial topic in mathematics that deals with the measurement of geometric figures and their properties. Understanding mensuration is essential for students as it frequently appears in school exams and competitive assessments. Practicing MCQs and objective questions in mensuration not only enhances conceptual clarity but also boosts confidence, helping students score better in their exams.
What You Will Practise Here
Area and perimeter of basic shapes like squares, rectangles, and triangles
Volume and surface area of three-dimensional figures such as cubes, cylinders, and spheres
Formulas for calculating areas and volumes
Real-life applications of mensuration concepts
Understanding and interpreting diagrams related to mensuration
Problem-solving techniques for complex mensuration questions
Important mensuration questions for exams
Exam Relevance
Mensuration is a significant part of the mathematics syllabus in CBSE, State Boards, NEET, and JEE. Students can expect questions related to the calculation of areas and volumes, often presented in multiple-choice formats. Common question patterns include direct calculations, application-based problems, and questions that require the use of formulas in real-world scenarios. Mastering mensuration can greatly enhance your performance in these examinations.
Common Mistakes Students Make
Confusing the formulas for area and perimeter, leading to incorrect answers
Overlooking units of measurement, which can affect the final result
Misinterpreting the dimensions given in word problems
Failing to visualize the shapes, which can complicate calculations
Not practicing enough variety in objective questions, limiting exposure to different problem types
FAQs
Question: What are some important Mensuration MCQ questions to focus on?Answer: Focus on questions related to calculating areas and volumes of common shapes, as well as application-based problems that relate to real-life scenarios.
Question: How can I improve my understanding of Mensuration concepts?Answer: Regular practice of objective questions and solving previous years' exam papers can significantly enhance your understanding and retention of mensuration concepts.
Start your journey towards mastering mensuration today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Your success in mathematics begins with a strong foundation in mensuration!
Q. A circle has a diameter of 14 m. What is its area? (Use π = 3.14)
A.
153.86 m²
B.
154 m²
C.
150 m²
D.
160 m²
Show solution
Solution
Radius = diameter / 2 = 14 m / 2 = 7 m. Area = π × radius² = 3.14 × (7 m)² = 3.14 × 49 m² = 153.86 m².
Correct Answer:
A
— 153.86 m²
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Q. A cone has a radius of 2 cm and a height of 6 cm. What is its volume?
A.
12.57 cm³
B.
25.13 cm³
C.
8.42 cm³
D.
16.76 cm³
Show solution
Solution
Volume = (1/3)πr²h = (1/3)π(2)²(6) = (1/3)π(4)(6) = 8π ≈ 25.13 cm³.
Correct Answer:
B
— 25.13 cm³
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Q. A cone has a radius of 2 cm and a height of 9 cm. What is its volume?
A.
12π cm³
B.
18π cm³
C.
24π cm³
D.
36π cm³
Show solution
Solution
Volume = 1/3 × πr²h = 1/3 × π × (2 cm)² × 9 cm = 12π cm³.
Correct Answer:
B
— 18π cm³
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Q. A cone has a radius of 3 cm and a height of 4 cm. What is its volume?
A.
12π cm³
B.
36π cm³
C.
9π cm³
D.
18π cm³
Show solution
Solution
Volume = 1/3 × πr²h = 1/3 × π × (3 cm)² × 4 cm = 12π cm³.
Correct Answer:
A
— 12π cm³
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Q. A cone has a radius of 4 cm and a height of 9 cm. What is its volume?
A.
75.40 cm³
B.
113.10 cm³
C.
113.04 cm³
D.
150.80 cm³
Show solution
Solution
Volume = (1/3)πr²h = (1/3)π(4)²(9) = 48π ≈ 150.80 cm³.
Correct Answer:
B
— 113.10 cm³
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Q. A cone has a radius of 5 cm and a height of 12 cm. What is its volume?
A.
78.54 cm³
B.
94.25 cm³
C.
100.00 cm³
D.
120.00 cm³
Show solution
Solution
Volume = (1/3)πr²h = (1/3)π(5)²(12) = 100π/3 ≈ 104.72 cm³
Correct Answer:
B
— 94.25 cm³
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Q. A cube has a side length of 4 cm. What is its surface area?
A.
16 cm²
B.
32 cm²
C.
64 cm²
D.
48 cm²
Show solution
Solution
Surface Area = 6a² = 6(4)² = 96 cm²
Correct Answer:
C
— 64 cm²
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Q. A cylinder has a height of 10 cm and a base radius of 2 cm. What is its surface area?
A.
75.40 cm²
B.
62.83 cm²
C.
40.00 cm²
D.
50.27 cm²
Show solution
Solution
Surface Area = 2πr(h + r) = 2π(2)(10 + 2) = 2π(2)(12) = 48π ≈ 150.80 cm².
Correct Answer:
A
— 75.40 cm²
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Q. A sphere has a diameter of 10 cm. What is its surface area?
A.
314.16 cm²
B.
250.00 cm²
C.
200.00 cm²
D.
150.00 cm²
Show solution
Solution
Surface Area = 4πr² = 4π(5)² = 100π ≈ 314.16 cm²
Correct Answer:
A
— 314.16 cm²
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Q. A sphere has a radius of 4 cm. What is its volume?
A.
32π cm³
B.
64π cm³
C.
48π cm³
D.
16π cm³
Show solution
Solution
Volume = (4/3)πr³ = (4/3)π × (4 cm)³ = 64π cm³.
Correct Answer:
A
— 32π cm³
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Q. A sphere has a radius of 5 cm. What is its volume?
A.
100π/3 cm³
B.
125π/3 cm³
C.
150π/3 cm³
D.
75π/3 cm³
Show solution
Solution
Volume = (4/3)πr³ = (4/3)π × (5 cm)³ = (4/3)π × 125 cm³ = 125π/3 cm³.
Correct Answer:
B
— 125π/3 cm³
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Q. A square has a perimeter of 40 cm. What is the length of one side?
A.
10 cm
B.
8 cm
C.
12 cm
D.
6 cm
Show solution
Solution
Perimeter = 4 × side, so side = Perimeter / 4 = 40 cm / 4 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. A triangle has a base of 8 cm and a height of 5 cm. What is its area?
A.
20 cm²
B.
30 cm²
C.
40 cm²
D.
50 cm²
Show solution
Solution
Area = 1/2 × base × height = 1/2 × 8 cm × 5 cm = 20 cm².
Correct Answer:
A
— 20 cm²
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Q. A triangle has an area of 24 m² and a base of 8 m. What is the height?
A.
6 m
B.
8 m
C.
4 m
D.
3 m
Show solution
Solution
Area = (base × height) / 2, so height = (2 × Area) / base = (2 × 24 m²) / 8 m = 6 m.
Correct Answer:
A
— 6 m
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Q. A triangle has an area of 36 m² and a base of 12 m. What is the height?
A.
4 m
B.
6 m
C.
8 m
D.
10 m
Show solution
Solution
Area = (base × height) / 2, so height = (2 × Area) / base = (2 × 36 m²) / 12 m = 6 m.
Correct Answer:
B
— 6 m
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Q. A triangle has an area of 48 m² and a base of 16 m. What is the height?
A.
4 m
B.
6 m
C.
8 m
D.
10 m
Show solution
Solution
Area = (base × height) / 2. Therefore, height = (2 × Area) / base = (2 × 48 m²) / 16 m = 6 m.
Correct Answer:
C
— 8 m
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Q. A triangle has an area of 50 m² and a base of 10 m. What is the height?
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Show solution
Solution
Area = (base × height) / 2, so height = (2 × Area) / base = (2 × 50 m²) / 10 m = 10 m.
Correct Answer:
A
— 5 m
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Q. A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What is its area?
A.
30 cm²
B.
60 cm²
C.
40 cm²
D.
50 cm²
Show solution
Solution
This is a right triangle. Area = (base × height) / 2 = (5 cm × 12 cm) / 2 = 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 its area?
A.
24 cm²
B.
30 cm²
C.
36 cm²
D.
40 cm²
Show solution
Solution
Using Heron's formula, s = (6 + 8 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12 × 6 × 4 × 2] = √[576] = 24 cm².
Correct Answer:
B
— 30 cm²
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Q. Calculate the surface area of a cylinder with a radius of 2 cm and a height of 10 cm.
A.
75.40 cm²
B.
62.83 cm²
C.
40.00 cm²
D.
50.27 cm²
Show solution
Solution
Surface Area = 2πr(h + r) = 2π(2)(10 + 2) = 2π(2)(12) = 48π ≈ 150.80 cm².
Correct Answer:
A
— 75.40 cm²
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Q. Calculate the surface area of a cylinder with a radius of 3 cm and a height of 10 cm.
A.
60 cm²
B.
62.83 cm²
C.
94.25 cm²
D.
100.00 cm²
Show solution
Solution
Surface Area = 2πr(h + r) = 2π(3)(10 + 3) = 2π(3)(13) = 78π ≈ 245.04 cm²
Correct Answer:
C
— 94.25 cm²
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Q. Calculate the surface area of a cylinder with a radius of 5 cm and a height of 10 cm.
A.
314.16 cm²
B.
250.00 cm²
C.
200.00 cm²
D.
150.00 cm²
Show solution
Solution
Surface Area = 2πr(h + r) = 2π(5)(10 + 5) = 2π(5)(15) = 150π ≈ 471.24 cm²
Correct Answer:
A
— 314.16 cm²
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Q. Calculate the surface area of a sphere with a radius of 6 cm.
A.
113.10 cm²
B.
150.80 cm²
C.
452.39 cm²
D.
226.20 cm²
Show solution
Solution
Surface Area = 4πr² = 4π(6)² = 144π ≈ 452.39 cm².
Correct Answer:
C
— 452.39 cm²
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Q. Find the surface area of a cone with a radius of 3 cm and a slant height of 5 cm.
A.
37.68 cm²
B.
28.26 cm²
C.
47.12 cm²
D.
50.27 cm²
Show solution
Solution
Surface Area = πr(l + r) = π(3)(5 + 3) = 24π ≈ 75.40 cm².
Correct Answer:
A
— 37.68 cm²
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Q. Find the surface area of a cone with a radius of 4 cm and a slant height of 5 cm.
A.
25.12 cm²
B.
50.24 cm²
C.
62.83 cm²
D.
78.54 cm²
Show solution
Solution
Surface Area = πr(l + r) = π(4)(5 + 4) = π(4)(9) = 36π ≈ 113.10 cm²
Correct Answer:
B
— 50.24 cm²
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Q. Find the volume of a rectangular prism with dimensions 3 cm, 4 cm, and 5 cm.
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
Show solution
Solution
Volume = lwh = 3 * 4 * 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
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Q. Find the volume of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm.
A.
60 cm³
B.
50 cm³
C.
40 cm³
D.
30 cm³
Show solution
Solution
Volume = lwh = 4 * 3 * 5 = 60 cm³.
Correct Answer:
B
— 50 cm³
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Q. Find the volume of a rectangular prism with length 4 cm, width 3 cm, and height 2 cm.
A.
24 cm³
B.
12 cm³
C.
20 cm³
D.
30 cm³
Show solution
Solution
Volume = lwh = 4 * 3 * 2 = 24 cm³.
Correct Answer:
B
— 12 cm³
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Q. Find the volume of a sphere with a radius of 7 cm.
A.
143.67 cm³
B.
153.94 cm³
C.
180.79 cm³
D.
200.00 cm³
Show solution
Solution
Volume = (4/3)πr³ = (4/3)π(7)³ ≈ 143.67 cm³
Correct Answer:
B
— 153.94 cm³
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Q. If the area of a triangle is 24 cm² and the height is 6 cm, what is the base?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
Area = (base × height) / 2, so base = (2 × Area) / height = (2 × 24 cm²) / 6 cm = 8 cm.
Correct Answer:
C
— 8 cm
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