Coordinate Geometry - SSC

What is the length of the arc of a circle whose radius is 35 cm and arc subtends an angle of 36° at the centre of the circle?

(Take π = 22/7)

• A.

  44 cm

• B.

  22 cm

• C.

  10 cm

• D.

  220 cm

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A solid metallic cube of side is $6\sqrt[3]{4}$ cm, is melted and recast into a cuboid of length 12 cm and breadth 9 cm. What is the length (in cm) of the longest diagonal of the cuboid?

• A.

  19

• B.

  18

• C.

  15

• D.

  17

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If the curved surface area of a closed cylinder is 225 cm² and the area of its base is 169 cm², then find the total surface area of the cylinder.

• A.

  394 cm²

• B.

  343 cm²

• C.

  563 cm²

• D.

  195 cm²

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In the following figure, ∆ABC is an inscribed triangle as shown and DE is an tangent to the circle at C. If m∠ACD = 65° and m∠ACB = 35°, find the measure of m∠BAC

​​​​​​​​​​​​​​

• A.

  80°

• B.

  75°

• C.

  60°

• D.

  65°

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If two supplementary angles differ by 74°, then one of the angles is:

• A.

  65°

• B.

  55°

• C.

  43°

• D.

  53°

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A wall 10 m long, 5 m high and 20 cm thick is to be constructed using bricks of dimensions 25 cm × 20 cm × 10 cm. How many bricks are required?

• A.

  2450

• B.

  2000

• C.

  2500

• D.

  2050

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The total surface area of a solid cylinder whose radius is r cm and height $\frac{r}{2}$ cm (in cm²) is:

• A.

  3π$\frac{r^2}{2}$

• B.

  4πr²

• C.

  3πr²

• D.

  3π$\frac{r^3}{2}$

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The diameter of the base and the slant height of a right circular cone are 10 cm and 16 cm, respectively.

Find its total surface area.

[Use π = 22/7]

• A.

  $\frac{5720}{7}$ cm²

• B.

  $\frac{720}{7}$ cm²

• C.

  330 cm²

• D.

  $\frac{1760}{7}$ cm²

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The maximum number of 4m 50 cm 20 cm slabs that may be stored in a 16m long, 12m wide, and 4m deep trench is:

• A.

  1910

• B.

  1890

• C.

  1960

• D.

  1920

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If the length of the diagonal of a cube is $6\sqrt{3}$ cm, then the length of the edge of the cube is:

• A.

  6 cm

• B.

  4 cm

• C.

  2 cm

• D.

  3 cm

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If a solid piece of iron in the form of a cuboid, of dimensions 49 cm 33 cm 24 cm, is moulded to form a solid sphere, then the radius of the sphere is ______.

[Use π = 22/7]

• A.

  16 cm

• B.

  10 cm

• C.

  18 cm

• D.

  21 cm

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The volume of a cube is 5832 cm³. Find its total surface area.

• A.

  1944 cm²

• B.

  1672 cm²

• C.

  1824 cm²

• D.

  1536 cm²

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A metallic solid cuboid of dimensions 36 cm × 18 cm × 12 cm is melted and recast in the form of cubes of side 6 cm. Find the number of cubes so formed.

• A.

  38

• B.

  40

• C.

  34

• D.

  36

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The sum of the length, breadth and depth of a cuboid is 23 cm, and its diagonal is 5√7 cm. Its surface area is:

• A.

  144 cm²

• B.

  177 cm²

• C.

  188 cm²

• D.

  111 cm²

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Find the total surface area of a cuboid whose length is 20 cm, width is 15 cm, and height is 8 cm.

• A.

  1160 cm²

• B.

  990 cm²

• C.

  1120 cm²

• D.

  1080 cm²

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The diagonal of a cube is 24 cm. Find its total surface area.

• A.

  1152 cm²

• B.

  1252 cm²

• C.

  1100 cm²

• D.

  1366 cm²

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Calculate the area of the quadrilateral formed with the vertices (-3,2),(5,4),(7,-6) and (-5,-4).

• A.

  80 square units

• B.

  160 square units

• C.

  0 square units

• D.

  150 square units

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How many 25 cm 11.25 cm 6 cm bricks will be required to construct an 8 m 6 m 22.5 cm wall?

(ignoring other material used)

• A.

  7020

• B.

  6400

• C.

  5800

• D.

  6800

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If the height and slant height of a right circular cone are 8 cm and 10 cm, respectively, then the volume of the cone is (use 7t = f ): ( correct the two decimal places)

• A.

  200 cm³

• B.

  301.71 cm³

• C.

  258 cm³

• D.

  299.45 cm³

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From the body of a solid cube of edge 7 cm, a solid sphere is removed. The volume of the remaining solid was found to be 163$\frac{1}{3}$ cm³. What is the diameter (in cm) of the sphere?

• A.

  5

• B.

  10

• C.

  8

• D.

  7

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Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:

• A.

  1 : $\sqrt{3}$

• B.

  3 : 1

• C.

  1 : 3

• D.

  $\sqrt{3}$ : 1

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Chords AB and CD of a circle, when produced, meet at the point P. If AB = 6.3 cm, BP= 4.5 cm, and CD= 3.6 cm, then the length (in cm) of PD is

• A.

  4.8cm

• B.

  3.5 cm

• C.

  3.1 cm

• D.

  5.4 cm

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A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic sphere of radius 12 cm is dropped into it. What will be the increase in the level of water in the vessel (in cm)?

• A.

  27

• B.

  9

• C.

  72

• D.

  2.25

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If the length of a diagonal of a square is ( a+b ), then the area of the square is:

• A.

  $a^2$ + $b^2$

• B.

  $\frac{1}{2}$(a² + b²)

• C.

  $\frac{1}{2}$(a² + b²) + ab

• D.

  a² + b² + 2ab

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What is the difference in the volume (in cm³) of a sphere of radius 7 cm and that of a cone of radius 7 cm and height 10 cm?

(use π = 22/7)

• A.

  205

• B.

  704

• C.

  924

• D.

  1078

• View Answer