Welcome to the Class 9 Math Chapter 11 Competitive Exam Quiz
Test your conceptual understanding and speed with these high-yield Previous Year Questions (PYQs) curated for RRB, SSC, and GD exams based on Class 9 Mensuration, Surface Areas, and Volumes.
Q1. The total surface area of a cone having radius r/2 and slant height 2l is:
- A) πr(l + r/4)
- B) 2πr(l + r)
- C) πr(l + r)
- D) 2πrl
View Solution
Correct Answer: A) πr(l + r/4)
Step-by-step Solution:
Total Surface Area (TSA) of a cone = π × radius × (slant height + radius)
Here, Radius (R) = r/2 and Slant Height (L) = 2l.
TSA = π × (r/2) × [2l + (r/2)]
TSA = πr × [ (2l/2) + (r/4) ] = πr(l + r/4).
Q2. If the surface area of a sphere is 154 cm², then its volume is (Take π = 22/7):
- A) 179.67 cm³
- B) 143.73 cm³
- C) 215.38 cm³
- D) 310.25 cm³
View Solution
Correct Answer: A) 179.67 cm³
Step-by-step Solution:
Surface Area of Sphere = 4πr² = 154 cm²
4 × (22/7) × r² = 154
r² = (154 × 7) / 88 = 49 / 4
r = 7/2 = 3.5 cm
Volume = (4/3)πr³ = (4/3) × (22/7) × (7/2)³
Volume = (4/3) × (22/7) × (343/8) = 539/3 ≈ 179.67 cm³.
Q3. A right circular cylinder and a cone have equal bases and equal heights. What is the ratio of the volume of the cylinder to the volume of the cone?
- A) 1 : 3
- B) 3 : 1
- C) 1 : 1
- D) 2 : 3
View Solution
Correct Answer: B) 3 : 1
Step-by-step Solution:
Volume of Cylinder = πr²h
Volume of Cone = (1/3)πr²h
Ratio = (πr²h) / [(1/3)πr²h] = 1 / (1/3) = 3 : 1.
Q4. If the radius of a sphere is doubled, what is the percentage increase in its volume?
- A) 100%
- B) 300%
- C) 700%
- D) 800%
View Solution
Correct Answer: C) 700%
Step-by-step Solution:
Original Volume (V1) = (4/3)πr³
New Radius (R) = 2r
New Volume (V2) = (4/3)π(2r)³ = 8 × [(4/3)πr³] = 8 × V1
Increase in Volume = V2 - V1 = 8V1 - V1 = 7V1
Percentage Increase = (7V1 / V1) × 100% = 700%.
Q5. The length of the longest rod that can be placed in a room of dimensions 12 m × 9 m × 8 m is:
- A) 17 m
- B) 15 m
- C) 29 m
- D) 13 m
View Solution
Correct Answer: A) 17 m
Step-by-step Solution:
Length of the longest rod = Diagonal of the cuboid room
Diagonal = √(length² + breadth² + height²)
Diagonal = √(12² + 9² + 8²) = √(144 + 81 + 64) = √289 = 17 m.
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