PlacementPrepA garden is 27 m long and 11 m wide. A path 2 m wide runs around it on the outside. What is the area of the path?
Solution
Outer rectangle = (27 + 4) × (11 + 4) = 465 m².
Path = 465 − 297 = 168 m².
Answer: (A) 168 m²
Quantitative Aptitude · Geometry
Mensuration: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
The circumference of a circle is 220 cm. What is its area? (Take π = 22/7)
Solution
2πr = 220 gives r = 35 cm.
Area = 22/7 × 35² = 3850 cm².
Answer: (A) 3850 cm²
The total surface area of a cube is 54 cm². What is its volume?
Solution
6a² = 54, so a² = 9 and a = 3 cm.
Volume = a³ = 27 cm³.
Answer: (C) 27 cm³
What is the volume of a cylinder with radius 14 cm and height 19 cm? (π = 22/7)
Solution
Volume = πr²h = 22/7 × 14² × 19 = 11,704 cm³.
Answer: (D) 11,704 cm³
What is the area of a triangle with sides 9 cm, 12 cm and 15 cm?
Solution
s = (9 + 12 + 15)/2 = 18.
Area = √(s(s−a)(s−b)(s−c)) = √(18 × 9 × 6 × 3) = 54 cm².
Answer: (B) 54 cm²
If each side of a square is increased by 25%, by what percentage does its area increase?
Solution
New area = (1 + 25/100)² = 25/16 times the old area.
Increase = 56.25%.
Answer: (D) 56.25%
A cone has radius 5 cm and height 12 cm. What is its slant height?
Solution
Slant height = √(r² + h²) = √(25 + 144) = 13 cm.
Answer: (A) 13 cm
A garden is 17 m long and 20 m wide. A path 4 m wide runs around it on the outside. What is the area of the path?
Solution
Outer rectangle = (17 + 8) × (20 + 8) = 700 m².
Path = 700 − 340 = 360 m².
Answer: (B) 360 m²
What is the area of a circle of radius 21 cm? (Take π = 22/7)
Solution
Area = πr² = 22/7 × 21 × 21 = 1386 cm².
Answer: (C) 1386 cm²
The total surface area of a cube is 384 cm². What is its volume?
Solution
6a² = 384, so a² = 64 and a = 8 cm.
Volume = a³ = 512 cm³.
Answer: (B) 512 cm³
What is the volume of a cylinder with radius 7 cm and height 12 cm? (π = 22/7)
Solution
Volume = πr²h = 22/7 × 7² × 12 = 1848 cm³.
Answer: (B) 1848 cm³
What is the area of a triangle with sides 7 cm, 24 cm and 25 cm?
Solution
s = (7 + 24 + 25)/2 = 28.
Area = √(s(s−a)(s−b)(s−c)) = √(28 × 21 × 4 × 3) = 84 cm².
Answer: (B) 84 cm²
If each side of a square is increased by 20%, by what percentage does its area increase?
Solution
New area = (1 + 20/100)² = 1.44 times the old area.
Increase = 44%.
Answer: (B) 44%
A cone has radius 6 cm and height 8 cm. What is its slant height?
Solution
Slant height = √(r² + h²) = √(36 + 64) = 10 cm.
Answer: (B) 10 cm
A garden is 24 m long and 22 m wide. A path 4 m wide runs around it on the outside. What is the area of the path?
Solution
Outer rectangle = (24 + 8) × (22 + 8) = 960 m².
Path = 960 − 528 = 432 m².
Answer: (A) 432 m²
The circumference of a circle is 132 cm. What is its area? (Take π = 22/7)
Solution
2πr = 132 gives r = 21 cm.
Area = 22/7 × 21² = 1386 cm².
Answer: (C) 1386 cm²
The total surface area of a cube is 1350 cm². What is its volume?
Solution
6a² = 1350, so a² = 225 and a = 15 cm.
Volume = a³ = 3375 cm³.
Answer: (A) 3375 cm³
What is the volume of a cylinder with radius 7 cm and height 11 cm? (π = 22/7)
Solution
Volume = πr²h = 22/7 × 7² × 11 = 1694 cm³.
Answer: (D) 1694 cm³
What is the volume of a cone with radius 7 cm and height 24 cm? (π = 22/7)
Solution
Volume = ⅓πr²h = ⅓ × 22/7 × 7² × 24 = 1232 cm³.
Answer: (C) 1232 cm³
A garden is 32 m long and 12 m wide. A path 3 m wide runs around it on the outside. What is the area of the path?
Solution
Outer rectangle = (32 + 6) × (12 + 6) = 684 m².
Path = 684 − 384 = 300 m².
Answer: (A) 300 m²
The total surface area of a cube is 96 cm². What is its volume?
Solution
6a² = 96, so a² = 16 and a = 4 cm.
Volume = a³ = 64 cm³.
Answer: (B) 64 cm³
What is the volume of a cylinder with radius 7 cm and height 13 cm? (π = 22/7)
Solution
Volume = πr²h = 22/7 × 7² × 13 = 2002 cm³.
Answer: (A) 2002 cm³
What is the area of a triangle with sides 5 cm, 12 cm and 13 cm?
Solution
s = (5 + 12 + 13)/2 = 15.
Area = √(s(s−a)(s−b)(s−c)) = √(15 × 10 × 3 × 2) = 30 cm².
Answer: (D) 30 cm²
A garden is 35 m long and 22 m wide. A path 3 m wide runs around it on the outside. What is the area of the path?
Solution
Outer rectangle = (35 + 6) × (22 + 6) = 1148 m².
Path = 1148 − 770 = 378 m².
Answer: (B) 378 m²
The total surface area of a cube is 726 cm². What is its volume?
Solution
6a² = 726, so a² = 121 and a = 11 cm.
Volume = a³ = 1331 cm³.
Answer: (D) 1331 cm³
What is the volume of a cylinder with radius 21 cm and height 20 cm? (π = 22/7)
Solution
Volume = πr²h = 22/7 × 21² × 20 = 27,720 cm³.
Answer: (B) 27,720 cm³
If each side of a square is increased by 50%, by what percentage does its area increase?
Solution
New area = (1 + 50/100)² = 2.25 times the old area.
Increase = 125%.
Answer: (C) 125%
A garden is 30 m long and 21 m wide. A path 3 m wide runs around it on the outside. What is the area of the path?
Solution
Outer rectangle = (30 + 6) × (21 + 6) = 972 m².
Path = 972 − 630 = 342 m².
Answer: (D) 342 m²
What is the volume of a cylinder with radius 21 cm and height 14 cm? (π = 22/7)
Solution
Volume = πr²h = 22/7 × 21² × 14 = 19,404 cm³.
Answer: (C) 19,404 cm³
If each side of a square is increased by 10%, by what percentage does its area increase?
Solution
New area = (1 + 10/100)² = 121/100 times the old area.
Increase = 21%.
Answer: (A) 21%
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