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CAT Quantitative Aptitude | CAT Geometry Mensuration

Mensuration is a fairly intuitive topic in CAT Geometry. Other than knowing basic formulae, structural and spatial understanding of the shapes helps one nail Mensuration questions in CAT exam. Mensuration comprises of 2D and 3D shapes including (but not limited to) Spheres, Cubes, Cuboids, Cylinders, Cones and more. You can expect at least one question from Mensuration in CAT exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

  1. CAT Geometry: Mensuration - Data sufficiency

    A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base the section has been made?
    Statement (I): H = 20 cm
    Statement (II): Volume of small cone: volume of large cone : 1:15

    1. If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone.
    2. If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together.
    3. If the question can be answered with either statement alone.
    4. If the question cannot be answered with the information provided.
    Choice B
    Can be answered only if both statements are used together.

  2. CAT Geometry: Mensuration - Sphere

    A sphere of radius r is cut by a plane at a distance of h from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere. Find h.

    1. r/√2
    2. r/√3
    3. r/√5
    4. r/√6
    Choice A

  3. CAT Geometry: Mensuration - Chords

    Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP = 6 cms, PB = 4 units and DP = 3 units. What is the area of the circle?

    1. 125π/4 sq cms
    2. 100π/7 sq cms
    3. 125π/8 sq cms
    4. 52π/3 sq cms
    Choice A
    125π/4 sq cms

  4. CAT Geometry: Mensuration - Cylinders

    Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?

    1. 15
    2. 17
    3. 22
    4. 21
    Choice D

  5. CAT Geometry: Mensuration - Triangles

    PQRS is a square of sides 2 cm & ST = 2 cm. Also, PT=RT. What is the area of ∆PST?
    Geometry - Mensuration: CAT Geometry Triangles Area

    1. 2 cm2
    2. √3 cm2
    3. √2 cm2
    4. 1/√2 cm2
    Choice C
    √2 cm2

  6. CAT Geometry: Mensuration - Length of string

    A string is wound around two circular disk as shown. If the radius of the two disk are 40 cm and 30 cm respectively. What is the total length of the string?
    Geometry - Mensuration: CAT Length of string

    1. 70 cm
    2. 70 + 165*π cm
    3. 70 + 120π cm
    4. 70 + 165*π/2 cm
    Choice D
    70 + 165*π/2 cm

  7. CAT Geometry: Mensuration - Cuboid

    Geometry - Mensuration: CAT Cuboid
    Figure above shows a box which has to be completely wrapped with paper. However, a single Sheet of paper need to be used without any tearing. The dimension of the required paper could be

    1. 17 cm by 4 cm
    2. 12 cm by 6 cm
    3. 15 cm by 4 cm
    4. 13 cm by 4 cm
    Choice B
    12 cm by 6 cm

  8. CAT Geometry: Mensuration - Right Circular Cone

    An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm3/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?

    1. 216π hours
    2. 1 hour
    3. 3 hours
    4. 36π hours
    Choice A
    216π hours

  9. CAT Geometry: Mensuration - Square and Triangle

    A square PQRS has an equilateral triangle PTO inscribed as shown:
    Geometry - Mensuration: CAT Square and triangle
    What is the ratio of A∆PQT to A∆TRU?

    1. 1 : 3
    2. 1 : √3
    3. 1 : √2
    4. 1 : 2
    Choice D
    1 : 2

  10. CAT Geometry: Mensuration - Spheres and Cubes

    A spherical shaped sweet is placed inside a cube of side 5 cm such that the sweet just fits the cube. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet?

    1. 2.5 cm
    2. 5(√3 – 1) cm
    3. 5(√2 – 1) cm
    4. 2.5(√3 – 1) cm
    Choice D
    2.5(√3 – 1) cm

  11. CAT Geometry: Mensuration - Square shape backyard

    Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?

    1. 4225
    2. 4096
    3. 4356
    4. Insufficient Data
    Choice C

  12. CAT Geometry: Mensuration - Circles

    PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters areas A and B are shaded A/B is equal to
    Geometry - Mensuration: CAT Circles

    1. π
    2. 1
    3. π/4
    4. 2
    Choice B

  13. CAT Geometry: Mensuration - Square

    ABCD is a square drawn inside a square PQRS of sides 4 cm by joining midpoints of the sides PQ, QR, RS, SP. Another square is drawn inside ABCD similarly. This process is repeated infinite number of times. Find the sum of all the squares.

    1. 16 cm2
    2. 28 cm2
    3. 32 cm2
    4. Infinite
    Choice C
    32 cm2

  14. CAT Geometry: Mensuration - Pentagon and Circles

    PQRST is a pentagon in which all the interior angles are unequal. A circle of radius ‘r’ is inscribed in each of the vertices. Find the area of portion of circles falling inside the pentagon.

    1. πr2
    2. 1.5πr2
    3. 2πr2
    4. 1.25πr2
    Choice B

  15. CAT Geometry: Mensuration - Circles

    Three circles with radius 2 cm touch each other as shown :-
    Geometry - Mensuration: CAT Circles
    Find the area of the circle, circumscribing the above figure.

    1. 3π(4+√3)2
    2. π/2(4+2√3)2
    3. π/4(4+2√3)22
    4. 12π−π/2(4+2√3)2
    Choice C

  16. CAT Geometry: Mensuration - Concentric Circles

    There are 5 concentric circles that are spaced equally from each other by 1.25 cms. The innermost circle has a square of side √(32) cm inscribed in it. If a square needs to be inscribed in the outermost circle, what will be its area?

    1. 324 sq. cm.
    2. (66 + 40√2) sq. cm
    3. 210.125 sq. cm.
    4. 162
    Choice D

  17. CAT Geometry: Mensuration - Cross section of sphere

    A spherical rubber ball of radius 14 cm is cut by a knife at a distance of “x” cm from its centre, into 2 different pieces. What should be the value of “x” such that the cumulative surface area of the newly formed pieces is 3/28 more than the rubber ball’s original surface area?

    1. 11.4 cm
    2. 3 cm
    3. 12.4 cm
    4. 7.5 cm
    Choice C
    12.4 cm

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