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
Option (C)
Solution
From CAT 2017 – Quantitative Aptitude – Geometry – Mensuration, we can see that,
Given, the non-parallel sides are equal. Let the non-parallel sides be x cm each
x= √(12^2 + 5^2) = 13
So, we have 6 faces, out of which 2 are trapezoid faces and 4 are rectangular faces.
Area of trapezium = 1/2(sum of two parallel sides)(height)
Area of 2 trapeziums
= 2[(1/2)(12)(10+20)] = 360 cm^2
Area of rectangle = base*height
Area of 4 rectangles
= 2[13 × 20] + 20(20) + 10(20) = 1120 cm^2
Total area = 1120 + 360 = 1480 cm^2
Option (C)
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