Quantitative Aptitude - Geometry - Mensuration - The base of a vertical pillar
Quantitative Aptitude - Geometry - Mensuration
Question
The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is
A) 1300
B) 1340
C) 1480
D) 1520
Answer

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Quantitative Aptitude - Geometry - Mensuration - A ball of diameter 4 cm
Quantitative Aptitude - Geometry - Mensuration
Question
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 Ï€ cm^3 . Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is
Answer
6
Solution
As per the question from CAT 2017 - Quantitative Aptitude - Geometry - Mensuration,
The height of the cylinder (h) = 3
The volume = 9Ï€

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Quantitative Aptitude - Geometry - Mensuration - A solid metallic cube
Quantitative Aptitude - Geometry - Mensuration
Question
A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to
A) 10
B) 50
C) 60
D) 20
Answer
Option (B)
Solution
As per the question from CAT 2017 - Quantitative Aptitude - Geometry - Mensuration,
Ratio of volumes of 5 sm

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Quantitative Aptitude â€“ Geometry - Mensuration â€“ A parallelogram ABCD has area 48 sqcm
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ A parallelogram ABCD has area 48 sqcm
A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?
a) 5â‰¤sâ‰¤7
b) sâ‰¤6
c) sâ‰¥6
d) sâ‰ 6
Answer: c) sâ‰¥6
Solution: 1
Solution: As the area of ABCD = 48=sÃ—h ------------1)
In right-angled triangle CKD, DK â‰¤ CD ( CD is hyp

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Quantitative Aptitude â€“ Geometry - Mensuration â€“ The area of a rectangle and the square
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ The area of a rectangle and the square
The area of a rectangle and the square of its perimeter are in the ratio 1 âˆ¶ 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio?
a) 1:3
b) 3:8
c) 2:9
d) 1:4
Answer: d) 1 : 4
Solution:
Given ratio of areas of rectangle and square = 1:25 = 4âˆ¶ 100=(1Ã—4):(10Ã—10)
Thus possible ratio

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Quantitative Aptitude â€“ Geometry - Mensuration â€“ Let ABCD be a rectangle inscribed in a circle
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ Let ABCD be a rectangle inscribed in a circle
Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
a) 25, 10
b) 24, 12
c) 25, 9
d) 24, 10
Answer: d) 24, 10
Solution:
As ABCD is a rectangle angles A,B,C and D will be 90Â°. Thus AC will be diameter of

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Quantitative Aptitude â€“ Geometry - Mensuration â€“ Given an equilateral triangle T1 with side 24 cm
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ Given an equilateral triangle T1 with side 24 cm
Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3

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Quantitative Aptitude â€“ Geometry - Mensuration â€“ Points E, F, G, H lie on the sides
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ Points E, F, G, H lie on the sides
Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is?
a) 2 : 5
b) 4 : 9
c) 3 : 8
d) 1 : 3
Solution:
in triangle EBF ,EF^2=x^2+(a-x)^2
Ratio of Areas = AB^2:

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Quantitative Aptitude â€“ Geometry - Mensuration â€“ A right circular cone of height 12 ft
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ A right circular cone of height 12 ft
A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With Ï€ = 22/7, the volume, in cubic ft, of the remaining part of the cone is (TITA)?
Answer: 198
Solution:
Volume of remaining part ( Aâ€™Bâ€™BA) = 1/3

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