Circles - SSC

The radii of two concentric circles with centre O are 26 cm and 16 cm. Chord AB of the larger circle is tangent to the smaller circle ar C and AD is a diameter. What is the length of D?

• A.

  42 cm

• B.

  36 cm

• C.

  35 cm

• D.

  38 cm

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O is the centre of a circle of radius 10 cm. P is a point outside the circle and PQ is a tangent to the circle. What is the length (in cm) of PQ if the length OP is 26 cm?

• A.

  $2\sqrt{194}$

• B.

  20

• C.

  25

• D.

  24

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Find the total surface area of a solid hemisphere whose radius is 4.2 cm.

(Take π = 22/7)

• A.

  266.32 cm²

• B.

  366.32 cm²

• C.

  166.32 cm²

• D.

  466.32 cm²

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 The surface area of a volleyball spherical is 100π cm². Find the volume of air enclosed in the ball.

• A.

  $\frac{400}{3}$π cm³

• B.

  $\frac{350}{3}$π cm³

• C.

  $\frac{500}{3}$π cm³

• D.

  $\frac{200}{3}$π cm³

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The total surface area of a hemisphere is 64.57 cm². Find its curved surface area.

• A.

  64.57 cm²

• B.

  53.44 cm²

• C.

  43.04 cm²

• D.

  33.04 cm²

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The surface area of a spherical balloon is 400 π cm². What is the volume of air in it?

• A.

  $\frac{4000}{3}$π cm³

• B.

  $\frac{1000}{3}$π cm³

• C.

  $\frac{3000}{3}$π cm³

• D.

  $\frac{400}{3}$π cm³

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 Find the volume of a cylinder whose diameter of base is 20 cm and height is two times that of the radius of its base.

• A.

  4000 cm³

• B.

  3000 cm³

• C.

  6000 cm³

• D.

  2000 cm³

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In the given figure, chords AB and CD intersect each other at point L Find CL.

​​​​​​​​​​​​​​

• A.

  6 cm

• B.

  7 cm

• C.

  4 cm

• D.

  5 cm

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What is the volume of a sphere whose diameter is 16.8 cm?

[Use π = 22/7]

• A.

  2487.312 cm³

• B.

  2473.812 cm³

• C.

  2483.712 cm³

• D.

  2483.172 cm³

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If the volume of a sphere is 972 π cm³, then find its radius.

• A.

  7 cm

• B.

  6 cm

• C.

  9 cm

• D.

  8 cm

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A pillar 11 m in radius is 21 m high. How much material was used to construct it?

(Use π = 22/7)

• A.

  7996 m³

• B.

  7886 m³

• C.

  7989 m³

• D.

  7986 m³

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The curved surface area of a hemisphere is 1232 cm². Its radius will be:

(Take π = 22/7)

• A.

  12 cm

• B.

  14 cm

• C.

  16 cm

• D.

  10 cm

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What is the surface area of a cylinder with base radius 2 cm and height 6 cm?

(Use π = 3.14)

• A.

  73 cm²

• B.

  88.24 cm²

• C.

  81 cm²

• D.

  75.36 cm²

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Find the surface area of a sphere of diameter 21 cm.

(Use π = 22/7)

• A.

  988 cm²

• B.

  1234 cm²

• C.

  1445 cm²

• D.

  1386 cm²

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What is the surface area of a sphere whose diameter is 16.8 cm?

[Use π = 22/7]

• A.

  877.04 cm²

• B.

  888.04 cm²

• C.

  878.04 cm²

• D.

  887.04 cm²

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As air is pumped into a spherical balloon, its radius increases from 7 cm to 14 cm.
Find the ratio of volume of the balloon's in both circumstances.

• A.

  2 : 5

• B.

  1 : 9

• C.

  1 : 8

• D.

  3 : 7

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The total surface area of a solid hemisphere is 16632 cm². Its volume is:

(Take π = 22/7)

• A.

  145232 cm³

• B.

  140232 cm³

• C.

  150032 cm³

• D.

  155232 cm³

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What is the volume of the largest right circular cone that can be cut out from a cube whose edge is 10 cm?

• A.

  $\frac{250\pi }{3}$ cm³

• B.

  $\frac{351\pi }{3}$ cm³

• C.

  $\frac{145\pi }{3}$ cm³

• D.

  $\frac{150\pi }{3}$ cm³

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Find the volume of a hemisphere of radius 21 cm.

(Use π = 22/7)

• A.

  19400 cm³

• B.

  18440 cm³

• C.

  17404 cm³

• D.

  19404 cm³

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A sphere passes through the eight corners of a cube of side 14 cm. Find the volume (in cm³) of the sphere.

Take π = 22/7

• A.

  4312$\sqrt{3}$

• B.

  4012$\sqrt{3}$

• C.

  4312$\sqrt{2}$

• D.

  4012$\sqrt{2}$

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In the following figure, ∆ABC is an inscribed triangle as shown and DE is a tangent to the circle at C. Which of the angles from the given options is necessarily equal to ∠ACD?

​​​​​​​​​​​​​​

• A.

  ∠BAC

• B.

  ∠BCE

• C.

  ∠ABC

• D.

  ∠BCA

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The radius of a circle is 90 cm. If the radius of this circle is increased to 99 cm, then what will be the percentage increase in the area of this circle?

• A.

  25%

• B.

  22.5%

• C.

  21%

• D.

  20%

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Points A and B are on a circle with centre O. PA and PB are tangents to the circle from an external point P. If PA and PB are inclined to each other at 42°, then find the measure of ∠OAB.

• A.

  21°

• B.

  69°

• C.

  42°

• D.

  25°

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The inner circumference of a circular path enclosed between two concentric circles is 264 m. The uniform width of the circular path is 3 m. What is the area (in , to the nearest whole number) of the path?

(Taken π = 22/7)

• A.

  948

• B.

  596

• C.

  820

• D.

  756

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PQ and RS are two parallel chords of a circle of length 14 cm and 48 cm. respectively, and lie on the same side of the centre O. If the distance between the chords is 17 cm, what is the radius (i.n cm) of the circle?

• A.

  25

• B.

  24

• C.

  28

• D.

  20

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