**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)

## Download CAT 2017 Question Paper with answers and detailed solutions in PDF

## CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Mensuration – Q1: 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 π cm^3 .

Quantitative Aptitude – Geometry – Mensuration – Q2: A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27.

Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

Quantitative Aptitude – Geometry – Coordinate – Q2: 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.

Quantitative Aptitude – Geometry – Circles – Q1: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is

Quantitative Aptitude – Geometry – Circles – Q2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.

Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.

Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.

Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is

Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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