Q. A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface area of the cone?
A.
50.24 cm²
B.
75.36 cm²
C.
100.48 cm²
D.
125.60 cm²
Show solution
Solution
Total Surface Area = πr(r + l), where l = √(r² + h²) = √(4² + 9²) = √(16 + 81) = √97. Total Surface Area = π * 4 * (4 + √97).
Correct Answer:
B
— 75.36 cm²
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Q. A cone has a base radius of 4 cm and a slant height of 5 cm. What is the lateral surface area of the cone?
A.
40π cm²
B.
20π cm²
C.
30π cm²
D.
25π cm²
Show solution
Solution
Lateral Surface Area = πrl = π * 4 * 5 = 20π cm².
Correct Answer:
A
— 40π cm²
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Q. A cone has a base radius of 5 cm and a height of 12 cm. What is the total surface area of the cone?
A.
130 cm²
B.
150 cm²
C.
180 cm²
D.
200 cm²
Show solution
Solution
Total Surface Area = πr(r + l), where l = √(r² + h²) = √(5² + 12²) = √169 = 13. Total Surface Area = π * 5 * (5 + 13) = 90π cm².
Correct Answer:
B
— 150 cm²
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Q. A cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone?
A.
12 cm³
B.
36 cm³
C.
24 cm³
D.
18 cm³
Show solution
Solution
Volume = (1/3)πr²h = (1/3) * π * 3² * 4 = (1/3) * 3.14 * 9 * 4 = 37.68 cm³.
Correct Answer:
C
— 24 cm³
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Q. A cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone? (Use π = 3.14)
A.
37.68 cm³
B.
12.56 cm³
C.
25.12 cm³
D.
18.84 cm³
Show solution
Solution
Volume = (1/3)πr²h = (1/3) * 3.14 * 3² * 4 = 37.68 cm³
Correct Answer:
A
— 37.68 cm³
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Q. A cube has a side length of 4 cm. What is the volume of the cube?
A.
16 cm³
B.
64 cm³
C.
48 cm³
D.
32 cm³
Show solution
Solution
Volume = side³ = 4³ = 64 cm³.
Correct Answer:
B
— 64 cm³
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Q. A cube has a volume of 27 cm³. What is the length of one side of the cube?
A.
3 cm
B.
4 cm
C.
5 cm
D.
6 cm
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Solution
Side = ∛Volume = ∛27 = 3 cm.
Correct Answer:
A
— 3 cm
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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the lateral surface area of the cylinder?
A.
40π cm²
B.
20π cm²
C.
30π cm²
D.
10π cm²
Show solution
Solution
Lateral Surface Area = 2πrh = 2 * π * 2 * 10 = 40π cm².
Correct Answer:
A
— 40π cm²
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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the volume of the cylinder?
A.
40π cm³
B.
20π cm³
C.
30π cm³
D.
10π cm³
Show solution
Solution
Volume = πr²h = π * 2² * 10 = π * 4 * 10 = 40π cm³.
Correct Answer:
A
— 40π cm³
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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the volume of the cylinder? (Use π = 3.14)
A.
40 cm³
B.
60 cm³
C.
80 cm³
D.
100 cm³
Show solution
Solution
Volume = πr²h = 3.14 * 2² * 10 = 125.6 cm³
Correct Answer:
B
— 60 cm³
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Q. A cylinder has a radius of 5 cm and a height of 10 cm. What is the total surface area of the cylinder?
A.
314 cm²
B.
150 cm²
C.
200 cm²
D.
250 cm²
Show solution
Solution
Total Surface Area = 2πr(h + r) = 2 * π * 5 * (10 + 5) = 2 * 3.14 * 5 * 15 = 471 cm².
Correct Answer:
A
— 314 cm²
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Q. A cylinder has a radius of 5 cm and a height of 12 cm. What is the total surface area of the cylinder?
A.
340 cm²
B.
400 cm²
C.
380 cm²
D.
420 cm²
Show solution
Solution
Total Surface Area = 2πr(h + r) = 2 * π * 5 * (12 + 5) = 2 * 3.14 * 5 * 17 = 530 cm².
Correct Answer:
A
— 340 cm²
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Q. A cylinder has a radius of 5 cm and a height of 7 cm. What is the total surface area of the cylinder?
A.
376.99 cm²
B.
314.16 cm²
C.
251.33 cm²
D.
157.08 cm²
Show solution
Solution
Total Surface Area = 2πr(h + r) = 2 * π * 5 * (7 + 5) = 2 * 3.14 * 5 * 12 = 376.99 cm².
Correct Answer:
A
— 376.99 cm²
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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank (including the top and bottom)?
A.
56.52 m²
B.
94.25 m²
C.
113.10 m²
D.
78.54 m²
Show solution
Solution
Surface Area = 2πr(h + r) = 2 * π * 3 * (5 + 3) = 2 * 3.14 * 3 * 8 = 150.72 m².
Correct Answer:
B
— 94.25 m²
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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank? (Use π = 3.14)
A.
56.52 m²
B.
94.2 m²
C.
94.5 m²
D.
47.1 m²
Show solution
Solution
Surface Area = 2πr(h + r) = 2 * 3.14 * 3 * (5 + 3) = 94.2 m²
Correct Answer:
B
— 94.2 m²
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Q. A hemisphere has a radius of 5 cm. What is the total surface area of the hemisphere?
A.
157.08 cm²
B.
100.00 cm²
C.
78.54 cm²
D.
314.16 cm²
Show solution
Solution
Total Surface Area = 3πr² = 3 * 3.14 * 5² = 3 * 3.14 * 25 = 157.08 cm².
Correct Answer:
A
— 157.08 cm²
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Q. A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is the total surface area of the box?
A.
70 cm²
B.
60 cm²
C.
100 cm²
D.
80 cm²
Show solution
Solution
Surface Area = 2(lw + lh + wh) = 2(10*5 + 10*2 + 5*2) = 2(50 + 20 + 10) = 2 * 80 = 160 cm².
Correct Answer:
A
— 70 cm²
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Q. A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is the volume of the box?
A.
100 cm³
B.
50 cm³
C.
20 cm³
D.
40 cm³
Show solution
Solution
Volume = length × width × height = 10 × 5 × 2 = 100 cm³
Correct Answer:
A
— 100 cm³
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Q. A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. What is the volume of the prism?
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
Show solution
Solution
Volume = length * width * height = 3 * 4 * 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
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Q. A rectangular prism has dimensions of 3 cm, 4 cm, and 5 cm. What is the total surface area?
A.
62 cm²
B.
60 cm²
C.
70 cm²
D.
50 cm²
Show solution
Solution
Surface Area = 2(lw + lh + wh) = 2(3*4 + 3*5 + 4*5) = 62 cm²
Correct Answer:
A
— 62 cm²
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Q. A rectangular prism has dimensions of 3 cm, 4 cm, and 5 cm. What is the volume of the prism?
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
Show solution
Solution
Volume = l * w * h = 3 * 4 * 5 = 60 cm³.
Correct Answer:
A
— 60 cm³
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Q. A sphere has a diameter of 10 cm. What is its volume? (Use π = 3.14)
A.
523.33 cm³
B.
314 cm³
C.
157.08 cm³
D.
78.5 cm³
Show solution
Solution
Volume = (4/3)πr³ = (4/3) * 3.14 * (5)³ = 523.33 cm³
Correct Answer:
A
— 523.33 cm³
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Q. A sphere has a radius of 7 cm. What is the surface area of the sphere?
A.
154 cm²
B.
308 cm²
C.
616 cm²
D.
44 cm²
Show solution
Solution
Surface Area = 4πr² = 4 * π * 7² = 4 * 3.14 * 49 = 615.44 cm².
Correct Answer:
B
— 308 cm²
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Q. A sphere has a radius of 7 cm. What is the volume of the sphere?
A.
143.67 cm³
B.
154.00 cm³
C.
200.00 cm³
D.
180.00 cm³
Show solution
Solution
Volume = (4/3)πr³ = (4/3) * 3.14 * 7³ = (4/3) * 3.14 * 343 = 1436.76 cm³.
Correct Answer:
A
— 143.67 cm³
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Q. What is the surface area of a cube with a side length of 6 cm?
A.
36 cm²
B.
72 cm²
C.
144 cm²
D.
24 cm²
Show solution
Solution
Surface Area = 6 * side² = 6 * 6² = 6 * 36 = 216 cm².
Correct Answer:
B
— 72 cm²
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Q. What is the surface area of a sphere with a diameter of 10 cm?
A.
100π cm²
B.
50π cm²
C.
25π cm²
D.
75π cm²
Show solution
Solution
Surface Area = 4πr² = 4π(5)² = 4π(25) = 100π cm².
Correct Answer:
A
— 100π cm²
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Q. What is the total surface area of a cube with a side length of 6 cm?
A.
72 cm²
B.
144 cm²
C.
36 cm²
D.
48 cm²
Show solution
Solution
Surface Area = 6 * side² = 6 * 6² = 6 * 36 = 216 cm².
Correct Answer:
B
— 144 cm²
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Q. What is the total surface area of a sphere with a radius of 7 cm? (Use π = 3.14)
A.
615.44 cm²
B.
153.86 cm²
C.
308 cm²
D.
154 cm²
Show solution
Solution
Surface Area = 4πr² = 4 * 3.14 * 7² = 615.44 cm²
Correct Answer:
A
— 615.44 cm²
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Showing 1 to 28 of 28 (1 Pages)
Volume and Surface Area MCQ & Objective Questions
Understanding "Volume and Surface Area" is crucial for students preparing for school exams and competitive tests in India. Mastering these concepts not only enhances your mathematical skills but also boosts your confidence in tackling objective questions. Practicing MCQs and important questions related to volume and surface area can significantly improve your exam performance and conceptual clarity.
What You Will Practise Here
Formulas for calculating volume and surface area of various geometric shapes
Definitions and properties of 3D figures like cubes, cylinders, cones, and spheres
Real-life applications of volume and surface area in problem-solving
Diagrams illustrating different shapes and their dimensions
Conversion between different units of measurement
Commonly asked objective questions and practice questions
Tips for quick calculations and avoiding common errors
Exam Relevance
The topic of volume and surface area is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to apply formulas, solve real-world problems, and interpret diagrams. Common question patterns include calculating the volume of solids, determining surface area, and solving multi-step problems that integrate these concepts.
Common Mistakes Students Make
Confusing the formulas for surface area and volume
Neglecting to convert units when necessary
Misinterpreting the dimensions given in word problems
Overlooking the importance of diagrams in understanding the shapes
Rushing through calculations, leading to simple arithmetic errors
FAQs
Question: What is the formula for the volume of a cylinder?Answer: The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height.
Question: How do I find the surface area of a sphere?Answer: The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere.
Now that you understand the significance of volume and surface area, it's time to put your knowledge to the test! Dive into our practice MCQs and important Volume and Surface Area questions for exams to solidify your understanding and excel in your studies.
