IPMPrepFind the curved surface area of a cylinder of radius 21 cm and height 8 cm (use π = 227), in sq cm.
Solution
CSA = 2πrh = 2 × (227) × 21 × 8 = 1056.
Answer: (A) 1056
Quantitative Ability · Geometry
Mensuration: IPMAT practice questions
24 questions, 6 of them short answer (type the number, as in IPMAT Indore). Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
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Find the volume of a cylinder of radius 3.5 cm and height 30 cm (use π = 227), in cubic cm.
Solution
V = πr2h = (227) × 3.52 × 30 = 1155.
Answer: (B) 1155
How many 1 cm cubes can be cut from a cube of edge 6 cm?
Solution
(61)3 = 63 = 216.
Answer: 216
A solid metal sphere of radius 10 cm is melted and recast into small spheres of radius 2 cm. How many small spheres are made?
Solution
Volume scales with the cube of the radius.
Number = (102)3 = 125.
Answer: (D) 125
A solid metal sphere of radius 8 cm is melted and recast into small spheres of radius 2 cm. How many small spheres are made?
Solution
Volume scales with the cube of the radius.
Number = (82)3 = 64.
Answer: (A) 64
A rectangular lawn is 23 m by 26 m. A path 2.5 m wide runs all round it on the inside. Find the area of the path in sq m.
Solution
Area of path = outer rectangle − inner rectangle.
= 598 − 378 = 220 sq m.
Answer: 220
If the radius of a circle increases by 20%, by what percentage does its area increase?
Solution
Area ∝ r2: (65)2 = 3625.
Increase = 44%.
Answer: (C) 44%
A solid metal sphere of radius 12 cm is melted and recast into small spheres of radius 2 cm. How many small spheres are made?
Solution
Volume scales with the cube of the radius.
Number = (122)3 = 216.
Answer: (D) 216
A rectangular lawn is 44 m by 17 m. A path 2.5 m wide runs all round it on the inside. Find the area of the path in sq m.
Solution
Area of path = outer rectangle − inner rectangle.
= 748 − 468 = 280 sq m.
Answer: (B) 280
A 8 cm cube is painted on all faces and cut into 2 cm cubes. How many small cubes have no paint at all?
Solution
There are 4 small cubes along each edge.
The unpainted ones form the inner (4 − 2)3 block: 8.
Answer: (D) 8
Find the curved surface area of a cylinder of radius 21 cm and height 30 cm (use π = 227), in sq cm.
Solution
CSA = 2πrh = 2 × (227) × 21 × 30 = 3960.
Answer: (A) 3960
Find the volume of a cone of radius 3.5 cm and height 16 cm (use π = 227), in cubic cm.
Solution
V = (13)πr2h = (13) × (227) × 3.52 × 16 = 205 13.
Answer: (D) 205 13
If the radius of a circle increases by 100%, by what percentage does its area increase?
Solution
Area ∝ r2: (2)2 = 4.
Increase = 300%.
Answer: (C) 300%
Find the total surface area of a cuboid 7 cm × 4 cm × 15 cm (in sq cm).
Solution
TSA = 2(lb + bh + hl) = 2(28 + 60 + 105) = 386.
Answer: (D) 386
If the radius of a sphere increases by 50%, by what percentage does its volume increase?
Solution
Volume ∝ r3: (32)3 = 278.
Increase = 237.5%.
Answer: (B) 237.5%
Find the curved surface area of a cylinder of radius 14 cm and height 16 cm (use π = 227), in sq cm.
Solution
CSA = 2πrh = 2 × (227) × 14 × 16 = 1408.
Answer: (A) 1408
A solid sphere of radius 6 cm is melted and drawn into a cylindrical wire of radius 3 cm. Find the length of the wire in cm.
Solution
(43)π × 63 = π × 32 × h.
h = 4 × 216/(3 × 9) = 32 cm.
Answer: (C) 32
A rectangular lawn is 21 m by 37 m. A path 1 m wide runs all round it on the inside. Find the area of the path in sq m.
Solution
Area of path = outer rectangle − inner rectangle.
= 777 − 665 = 112 sq m.
Answer: (D) 112
A 6 cm cube is painted on all faces and cut into 1 cm cubes. How many small cubes have no paint at all?
Solution
There are 6 small cubes along each edge.
The unpainted ones form the inner (6 − 2)3 block: 64.
Answer: 64
How many 2 cm cubes can be cut from a cube of edge 10 cm?
Solution
(102)3 = 53 = 125.
Answer: 125
If the radius of a sphere increases by 10%, by what percentage does its volume increase?
Solution
Volume ∝ r3: (1110)3 = 13311000.
Increase = 33.1%.
Answer: (D) 33.1%
A rectangular lawn is 24 m by 26 m. A path 2.5 m wide runs all round it on the outside. Find the area of the path in sq m.
Solution
Area of path = outer rectangle − inner rectangle.
= 899 − 624 = 275 sq m.
Answer: 275
A rectangular lawn is 17 m by 25 m. A path 2 m wide runs all round it on the outside. Find the area of the path in sq m.
Solution
Area of path = outer rectangle − inner rectangle.
= 609 − 425 = 184 sq m.
Answer: 184
If the radius of a circle increases by 10%, by what percentage does its area increase?
Solution
Area ∝ r2: (1110)2 = 121100.
Increase = 21%.
Answer: (D) 21%
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.