Mensuration

1

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 π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

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2

The surface area of a sphere is 616 square cm. If its radius is changed so that the area gets reduced 75% then the radius becomes

  1. 1.6 cm
  2. 2.3 cm
  3. 2.5 cm
  4. 3.5 cm
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3

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be

  1. 20 cm
  2. 25 cm
  3. 35 cm
  4. 50 cm
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4

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is

  1. 8960
  2. 5120
  3. 4830
  4. 6420
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5

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder equal their diameters. Then their volumes are proportional, respectively to

  1. 2 : 1 : 3
  2. 3 : 2 : 1
  3. 1 : 2 : 3
  4. 1 : 3 : 1
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6

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to

  1. 3
  2. 3.5
  3. 3
  4. 4.5
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7

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio

  1. 1 : 4
  2. 1 : 7
  3. 8 : 19
  4. 1 : 3
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8

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

  1. 2 : 5
  2. √3 : 2
  3. 3 : 4
  4. 1 : √3
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9

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.

  1. 168 m2
  2. 84 m2
  3. 42 m2
  4. 22 m2
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10

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

  1. 4 : 3
  2. 4 : 1
  3. 3 : 1
  4. 1 : 3
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11

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

  1. 17.05
  2. 22.45
  3. 26.25
  4. 27.85
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12

If a right circular cylinder of height 14 is inscribed in a sphere of radius 8, then the volume of the cylinder is

  1. 110
  2. 220
  3. 440
  4. 660
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13

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

  1. 3√2
  2. 3
  3. 4
  4. √3
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14

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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