CAT 2017 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Geometry Questions | Question 16

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Question 16 : 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

  1. 1300
  2. 1340
  3. 1480
  4. 1520

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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2017 Question Paper Quants Slot 2 Geometry

We have to find the total area of all six surfaces of the pillar which is 4 rectangles + 2 trapeziums one at the top and one at the bottom
Area of the rectangle = b × h
⟹ Area of rectangle with l = 20 b = 10
⟹ Area = 200 sq.cm
⟹ Area of rectangle with l = 20 b = 20
Area = 400 sq.cm
⟹ Area of 2 rectangles with l = 20 b = 13 is 2 × 13 × 20 = 520 sq. cm
Sum of areas of 4 rectangles = 520 + 200 + 400 = 1120 sq.cm
Area of the trapezium = \\frac{1}{2}) × 12 (10 + 20)
Area of the trapezium = 6 × 30 = 180 sq.cm
Area of both the trapezium = 2 × 180 = 360 sq.cm
Sum of areas of 4 rectangles = 1120 sq.cm.
Area of both the trapezium = 360 sq.cm
Total surface area of the pillar = 4 rectangles + 2 trapeziums
Total surface area of the pillar = 1120 + 360
Total surface area of the pillar = 1480 sq.cm

The question is "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"

Hence, the answer is 1480

Choice C is the correct answer

 

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