Geometry & Mensuration for Competitive Exam Success

Geometry & Mensuration

Area and Perimeter Problems Circle Theorems for Aptitude Volume of Solids

Q. A circle has a circumference of 62.8 cm. What is its radius?

A. 10 cm
B. 15 cm
C. 20 cm
D. 5 cm

Solution

Circumference = 2πr, so r = Circumference / (2π) = 62.8 / (2π) ≈ 10 cm.

Correct Answer: A — 10 cm

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Q. A circle has a radius of 3 cm. What is its area?

A. 28.26 cm²
B. 18.84 cm²
C. 31.42 cm²
D. 12.56 cm²

Solution

Area = π × radius² = π × (3 cm)² ≈ 28.26 cm².

Correct Answer: A — 28.26 cm²

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Q. A cube has a side length of 4 cm. What is its volume?

A. 16 cm³
B. 32 cm³
C. 64 cm³
D. 48 cm³

Solution

Volume = s³ = 4³ = 64 cm³.

Correct Answer: C — 64 cm³

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Q. A pyramid has a square base with a side length of 6 cm and a height of 9 cm. What is its volume?

A. 54 cm³
B. 72 cm³
C. 108 cm³
D. 36 cm³

Solution

Volume = (1/3) × base area × height = (1/3) × (6²) × 9 = 108 cm³.

Correct Answer: B — 72 cm³

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Q. A trapezoid has bases of 8 m and 5 m, and a height of 4 m. What is its area?

A. 26 m²
B. 30 m²
C. 20 m²
D. 24 m²

Solution

Area = (base1 + base2) × height / 2 = (8 m + 5 m) × 4 m / 2 = 26 m².

Correct Answer: A — 26 m²

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Q. Calculate the volume of a triangular prism with a base area of 10 cm² and a height of 8 cm.

A. 80 cm³
B. 40 cm³
C. 60 cm³
D. 20 cm³

Solution

Volume = base area × height = 10 × 8 = 80 cm³.

Correct Answer: A — 80 cm³

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Q. Find the volume of a sphere with a radius of 5 cm.

A. 33.51 cm³
B. 65.45 cm³
C. 523.60 cm³
D. 125.66 cm³

Solution

Volume = (4/3)πr³ = (4/3)π(5)³ = (500/3)π ≈ 523.60 cm³.

Correct Answer: C — 523.60 cm³

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Q. If a circle's area is 78.5 cm², what is its radius?

A. 5 cm
B. 7 cm
C. 6 cm
D. 4 cm

Solution

Area = πr², so r = √(Area/π) = √(78.5/π) ≈ 5 cm.

Correct Answer: B — 7 cm

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Q. If the diameter of a circle is 10 m, what is its circumference?

A. 31.4 m
B. 25.0 m
C. 20.0 m
D. 15.7 m

Solution

Circumference = πd = π(10) ≈ 31.4 m.

Correct Answer: A — 31.4 m

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Q. If the length of a rectangle is doubled and the width remains the same, how does the area change?

A. It doubles
B. It triples
C. It remains the same
D. It quadruples

Solution

Area = length × width; if length is doubled, area also doubles.

Correct Answer: A — It doubles

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Q. What is the area of a circle with a radius of 4 cm?

A. 16π cm²
B. 8π cm²
C. 12π cm²
D. 20π cm²

Solution

Area = π * r² = π * 4² = 16π cm².

Correct Answer: A — 16π cm²

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Q. What is the area of a parallelogram with a base of 10 cm and a height of 6 cm?

A. 60 cm²
B. 50 cm²
C. 40 cm²
D. 30 cm²

Solution

Area = base * height = 10 * 6 = 60 cm².

Correct Answer: A — 60 cm²

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Q. What is the area of a sector with a central angle of 90 degrees in a circle of radius 4 cm?

A. 6.28 cm²
B. 12.56 cm²
C. 3.14 cm²
D. 9.42 cm²

Solution

Area of sector = (θ/360) * πr² = (90/360) * π(4)² = (1/4) * 16π = 4π ≈ 12.56 cm².

Correct Answer: B — 12.56 cm²

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Q. What is the area of a trapezoid with bases of 6 cm and 10 cm, and a height of 4 cm?

A. 32 cm²
B. 24 cm²
C. 20 cm²
D. 28 cm²

Solution

Area = 1/2 * (base1 + base2) * height = 1/2 * (6 + 10) * 4 = 32 cm².

Correct Answer: B — 24 cm²

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Q. What is the distance between the points (3, 4) and (7, 1) in a coordinate plane?

A. 5 units
B. 4 units
C. 6 units
D. 7 units

Solution

Distance = √[(x2 - x1)² + (y2 - y1)²] = √[(7 - 3)² + (1 - 4)²] = √[16 + 9] = √25 = 5 units.

Correct Answer: A — 5 units

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Q. What is the length of an arc of a circle with a radius of 3 m and a central angle of 60 degrees?

A. 3.14 m
B. 3.77 m
C. 5.24 m
D. 6.28 m

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2π(3) = (1/6) * 6π = π ≈ 3.14 m.

Correct Answer: B — 3.77 m

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Q. What is the perimeter of a rectangle with length 10 m and width 4 m?

A. 28 m
B. 24 m
C. 20 m
D. 30 m

Solution

Perimeter = 2 × (length + width) = 2 × (10 m + 4 m) = 28 m.

Correct Answer: A — 28 m

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Q. What is the perimeter of a square with a side length of 4 m?

A. 12 m
B. 16 m
C. 20 m
D. 8 m

Solution

Perimeter = 4 × side = 4 × 4 m = 16 m.

Correct Answer: B — 16 m

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Q. What is the perimeter of a triangle with sides measuring 7 cm, 5 cm, and 9 cm?

A. 21 cm
B. 19 cm
C. 22 cm
D. 20 cm

Solution

Perimeter = side1 + side2 + side3 = 7 cm + 5 cm + 9 cm = 21 cm.

Correct Answer: A — 21 cm

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Q. What is the surface area of a sphere with a radius of 3 cm?

A. 36π cm²
B. 27π cm²
C. 12π cm²
D. 18π cm²

Solution

Surface Area = 4πr² = 4π * 3² = 36π cm².

Correct Answer: A — 36π cm²

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Q. What is the volume of a cone with a radius of 2 cm and a height of 6 cm?

A. 8.38 cm³
B. 12.57 cm³
C. 25.13 cm³
D. 16.76 cm³

Solution

Volume = (1/3)πr²h = (1/3)π(2)²(6) = 8π/3 ≈ 25.13 cm³.

Correct Answer: A — 8.38 cm³

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Q. What is the volume of a cylinder with a radius of 3 cm and a height of 7 cm?

A. 63π cm³
B. 21π cm³
C. 27π cm³
D. 30π cm³

Solution

Volume = π * r² * h = π * 3² * 7 = 63π cm³.

Correct Answer: A — 63π cm³

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Q. What is the volume of a frustum of a cone with a radius of 3 cm at the top, 5 cm at the bottom, and a height of 4 cm?

A. 40.84 cm³
B. 30.00 cm³
C. 50.24 cm³
D. 60.00 cm³

Solution

Volume = (1/3)πh(R² + Rr + r²) = (1/3)π(4)(5² + 5*3 + 3²) = (1/3)π(4)(25 + 15 + 9) = (1/3)π(4)(49) ≈ 40.84 cm³.

Correct Answer: A — 40.84 cm³

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Q. What is the volume of a hemisphere with a radius of 7 cm?

A. 143.67 cm³
B. 107.76 cm³
C. 153.94 cm³
D. 98.17 cm³

Solution

Volume = (2/3)πr³ = (2/3)π(7)³ = (686/3)π ≈ 143.67 cm³.

Correct Answer: A — 143.67 cm³

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Q. What is 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

Solution

Volume = l × w × h = 3 × 4 × 5 = 60 cm³.

Correct Answer: A — 60 cm³

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Geometry & Mensuration

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