Chapter 9 (Balbharati) · Class 9 Maharashtra SSC · MCQ Test
Surface Area and Volume (पृष्ठफळ आणि घनफळ) MCQ Test — Class 9 Maharashtra SSC
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Surface Area and Volume (पृष्ठफळ आणि घनफळ) — MCQ Questions
1A room's walls and ceiling need to be painted. The floor is not to be painted. The room is in the shape of a cuboid with length 'l', breadth 'b', and height 'h'. Which formula represents the total area to be painted?
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Answer: 2h(l + b) + lb
Hint: Think about which surfaces are included in the lateral surface area and which additional surface needs to be painted.
Solution:
The area of the four walls is the Lateral Surface Area (LSA) of the cuboid, which is 2h(l + b).
The ceiling is one of the faces with dimensions length (l) and breadth (b). Its area is lb.
Since the floor is not painted, the total area to be painted is the sum of the LSA and the area of the ceiling. — Total Area = LSA + Area of ceiling = 2h(l + b) + lb
2If the side length of a cube is doubled, how many times does its lateral surface area increase?
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Answer: 4 times
Hint: Recall the formula for the lateral surface area of a cube and see how it changes when the side length is multiplied by 2.
Solution:
Let the original side length of the cube be 'a'.
The original Lateral Surface Area (LSA) of the cube is 4a².
If the side length is doubled, the new side length becomes '2a'. The new LSA will be 4 × (2a)² = 4 × (4a²) = 16a².
Comparing the new LSA (16a²) to the original LSA (4a²), the increase is 16a² / 4a² = 4 times.
3A company wants to design a label for a cylindrical can of juice. The label will cover only the curved part of the can, from top to bottom. Which of the following geometric areas should the company calculate for the label?
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Answer: Curved Surface Area
Hint: Consider which part of the cylinder is being covered by the label. Does it include the top or bottom circular faces?
Solution:
The problem states that the label covers only the 'curved part' of the can, from top to bottom.
The curved part of a cylinder is specifically known as its Curved Surface Area (CSA).
The Total Surface Area would include the top and bottom circular bases, which are not covered by the label. Volume is the space occupied, not the surface.
4Ravi calculated the total surface area of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm, and got an answer of 62 cm². His teacher said his calculation was correct but mentioned he might have made a conceptual mistake in how he arrived at the formula. Which of the following statements likely describes Ravi's conceptual mistake?
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Answer: He calculated the sum of areas of only three unique faces and multiplied by 2, which is the correct approach.
Hint: Think about the formula for the total surface area of a cuboid and how it's derived from the areas of its faces. The question states his calculation was correct but implies a conceptual misunderstanding of the formula's derivation.
Solution:
The Total Surface Area (TSA) of a cuboid is 2(lb + bh + hl).
For l=5, b=3, h=2, TSA = 2(5×3 + 3×2 + 2×5) = 2(15 + 6 + 10) = 2(31) = 62 cm².
The correct calculation yields 62 cm². The statement implies a conceptual mistake in derivation, not the final number. The TSA formula is derived by finding the area of the three unique faces (lb, bh, hl) and then multiplying their sum by 2, because each face has an identical opposite face.
Therefore, if Ravi conceptually understood it as 'sum of unique faces multiplied by 2', it's the correct conceptual approach to derive the formula. The question's premise is tricky, suggesting Ravi *might* have made a conceptual mistake, even if the answer is correct. The correct option identifies the *correct* conceptual understanding as a potential 'mistake' if the teacher expected a different explanation, but it highlights that the approach leading to the correct answer *is* the standard derivation. This means options A, B, C describe actual errors that would lead to a wrong answer.
5Which of the following statements about the surface areas of a cube with side length 'a' is true?
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Answer: The LSA is 4a².
Hint: Remember that a cube has 6 faces in total. Lateral surface area excludes the top and bottom faces.
Solution:
A cube has 6 identical square faces, each with an area of a².
The Lateral Surface Area (LSA) includes the area of the four side faces. So, LSA = 4 × a² = 4a².
The Total Surface Area (TSA) includes the area of all six faces. So, TSA = 6 × a² = 6a².
Therefore, the statement 'The LSA is 4a²' is true.
6A cylindrical water tank has a volume of 1540 cm³ and a radius of 7 cm. What is the height of the tank? (Use π = 22/7)
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Answer: 10 cm
Hint: Recall the formula for the volume of a cylinder and rearrange it to solve for height.
Solution:
The formula for the volume of a cylinder is V = πr²h.
Given V = 1540 cm³, r = 7 cm, and π = 22/7, we can substitute these values into the formula: 1540 = (22/7) × (7)² × h.
Simplify the equation: 1540 = (22/7) × 49 × h => 1540 = 22 × 7 × h => 1540 = 154 × h.
Solve for h: h = 1540 / 154 = 10 cm.
7A student calculates the surface area of a box and writes the answer as 300 cm³. What mistake has the student made?
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Answer: The unit for surface area should be square units, not cubic units.
Hint: Think about the fundamental difference between surface area and volume and their respective units of measurement.
Solution:
Surface area measures the extent of a two-dimensional surface, even if it's on a 3D object.
The unit for any area measurement, including surface area, is always in square units (e.g., cm², m², km²).
Cubic units (e.g., cm³, m³) are used to measure volume, which is the amount of space an object occupies.
Therefore, using cm³ for surface area is a fundamental mistake in units.
8A gift box is shaped like a cuboid with length 20 cm, breadth 15 cm, and height 10 cm. If the box is open at the top, what is the total area of the cardboard required to make the box?
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Answer: 1000 cm²
Hint: Remember that the box is open at the top, so you need to subtract the area of one of the faces from the total surface area formula.
Solution:
The dimensions of the cuboid are l = 20 cm, b = 15 cm, h = 10 cm.
The total surface area (TSA) of a closed cuboid is 2(lb + bh + hl).
Since the box is open at the top, the area of the top face (lb) needs to be subtracted from the TSA.
Area of cardboard = TSA - Area of top face = 2(lb + bh + hl) - lb = 2(20×15 + 15×10 + 10×20) - (20×15).
Area = 2(300 + 150 + 200) - 300 = 2(650) - 300 = 1300 - 300 = 1000 cm².
Wait, I made a calculation error above. Let's recalculate: Area of cardboard = lb + 2(bh + hl) (Area of base + area of 4 walls) = (20×15) + 2(15×10 + 10×20) = 300 + 2(150 + 200) = 300 + 2(350) = 300 + 700 = 1000 cm².
Let's re-check the options and my calculation. The correct answer in my head was 950. Let's trace it again carefully. The problem is for an open box. This means it has 5 faces. The bottom face (lb) and the four walls (LSA = 2h(l+b)).
Area of cardboard = (Area of base) + (Lateral Surface Area) = (l × b) + 2h(l + b).
Area = (20 × 15) + 2 × 10 × (20 + 15).
Area = 300 + 20 × 35.
Area = 300 + 700 = 1000 cm².
My previous calculation of 1000 cm² was correct. Let me double check if option 950 cm² is correct for some other interpretation or if I have a different expected answer. The options are 600, 1100, 1000, 950. My derived answer is 1000. So the option should be C. Let me correct the `correctAnswer` to 1000 cm².
9Cylinder A has radius 'r' and height 'h'. Cylinder B has radius '2r' and height 'h/2'. Which of the following statements is true regarding their volumes?
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Answer: Volume of B is greater than Volume of A.
Hint: Write down the volume formulas for both cylinders using their given dimensions and then compare the two expressions.
Solution:
Volume of Cylinder A (VA) = πr²h.
Volume of Cylinder B (VB) = π(2r)²(h/2).
Simplify VB: VB = π(4r²)(h/2) = π(4/2)r²h = 2πr²h.
Comparing VA = πr²h and VB = 2πr²h, we see that VB = 2 × VA. Therefore, Volume of B is greater than Volume of A.
10A large cube with a side length of 6 cm is melted and recast into smaller cubes, each with a side length of 2 cm. How many smaller cubes can be formed?
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Answer: 27
Hint: When a solid is melted and recast, its volume remains conserved. Calculate the volume of the large cube and one small cube.
Solution:
The volume of the large cube = (side)³ = (6 cm)³ = 216 cm³.
The volume of one smaller cube = (side)³ = (2 cm)³ = 8 cm³.
When the large cube is melted and recast, the total volume of material remains the same. So, the total volume of all small cubes must equal the volume of the large cube.
Number of smaller cubes = (Volume of large cube) / (Volume of one smaller cube) = 216 cm³ / 8 cm³ = 27.
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Tips for Surface Area and Volume (पृष्ठफळ आणि घनफळ) MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Surface Area and Volume (पृष्ठफळ आणि घनफळ) MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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