Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

1. Q161
   The length ​of the ​minute hand of ​a clock is 14 ​cm. Find ​the ​area swept ​by the minute ​hand in 5 minutes.
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2. Q162
   A chord of ​a ​circle of radius $10$ cm subtends ​a ​right angle at the ​centre. Find the area of ​the corresponding:

   1. (i)minor ​segment,
   2. (ii)major ​sector. (Use $\pi =3.14$)
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3. Q163
   In a ​circle ​of radius ​21 cm, an arc subtends an angle of 60 deg ​at the centre. Find:

   1. (i)the length of the arc
   2. (ii)area of the sector formed ​by the arc ​
   3. (iii)area of the ​segment formed by the corresponding chord.
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4. Q164
   A chord of a ​circle of radius 15 cm subtends an angle of $60^{\circ }$ at the centre. Find the areas of the corresponding minor and major ​segments of ​the circle. (Use $\pi =3.14$ and $\sqrt{3}=1.73$)

   1. (i)The area of ​the ​corresponding minor segment.
   2. (ii)​The area of the corresponding major segment.
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5. Q165
   A chord of ​a circle of radius 12 ​cm subtends an angle ​of $120^{\circ }$ at the ​centre. Find ​the area of the ​corresponding ​segment of ​the circle. (Use $\pi =3.14$ and $\sqrt{3}=1.73$)
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6. Q166
   A horse is tied to a peg at one corner of ​a square shaped grass field of side ​15 m by means ​of ​a 5 m long rope (see Fig. 11.8). Find ​

   1. (i)the area of that part of the field in which the horse ​can graze.
   2. (ii)the increase in the grazing area if the rope were ​10 m long ​instead of 5 m. (Use $\pi =3.14$)
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7. Q167
   A brooch is made with silver ​wire in the form of a circle with ​diameter 35 ​mm. ​The wire ​is also used in making 5 diameters ​which divide the circle ​into 10 equal sectors as shown in Fig. 11.9. Find:

   1. (i)the ​total length of the silver wire required.
   2. (ii)the area of each sector of the brooch.

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8. Q168
   An ​umbrella has 8 ​ribs which are equally spaced (see ​Fig. ​11.10). Assuming ​umbrella to be a flat circle of radius 45 ​cm, find the area ​between the two consecutive ribs ​of the umbrella.

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9. Q169
   A car has ​two wipers which do ​not ​overlap. Each wiper has ​a blade of length 25 ​cm sweeping through an angle of $115^{\circ }$. ​Find ​the total area cleaned at each sweep ​of the blades.
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10. Q170
    To warn ships for underwater ​rocks, ​a lighthouse spreads a red coloured light over a ​sector of angle $80^{\circ }$ to a distance of $16.5$ km. ​Find the ​area ​of the ​sea over which the ships are warned. (Use $\pi =3.14$)
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11. Q171
    A round ​table ​cover has ​six equal designs as shown in Fig. 11.11. If ​the radius of the cover is 28 cm, find ​the cost of making ​the designs at the rate ​of $\text{Rs }0.35$ per cm${}^2$. ​(Use $\sqrt{3}=1.7$)
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12. Q172
    Tick the ​correct ​answer in the ​following: Area ​of a ​sector of angle $p$ (in degrees) of a ​circle ​with ​radius R is

    1. (a)$\frac{p}{180}\times 2\pi R$
    2. (b)$\frac{p}{180}\times \pi R^2$
    3. (c)$\frac{p}{360}\times 2\pi R$
    4. (d)$\frac{p}{720}\times 2\pi R^2$
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13. Q173
    2 ​cubes each of volume ​64 cm^3 are ​joined ​end to end. Find ​the ​surface ​area ​of the resulting cuboid.
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14. Q174
    A vessel ​is in ​the form of a hollow hemisphere mounted by a hollow ​cylinder. The diameter of ​the hemisphere is ​14 cm and ​the total height of ​the vessel is 13 cm. Find the inner surface area of the vessel.
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15. Q175
    A toy ​is in the form of ​a ​cone of radius 3.5 cm mounted ​on a ​hemisphere of same ​radius. The total height of the toy ​is 15.5 cm. Find the ​total surface area of the toy.
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16. Q176
    A cubical block of side 7 cm ​is surmounted by a hemisphere. What ​is ​the greatest ​diameter the ​hemisphere can ​have? ​Find the ​surface area of the solid.
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17. Q177
    A hemispherical depression ​is cut out from one face of ​a cubical wooden block such ​that the diameter $l$ of the hemisphere is equal to the edge of ​the cube. ​Determine ​the surface area of the remaining solid.
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18. Q178
    A medicine capsule is in the shape of a cylinder with ​two hemispheres stuck to each of its ends (see Fig. 12.10). ​The length of the entire ​capsule is 14 mm and ​the diameter ​of the capsule ​is ​5 mm. Find its surface area.
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19. Q179
    A tent is in the shape of a cylinder surmounted ​by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find ​the cost of the canvas ​of the tent at the rate of Rs 500 per m^2. (Note ​that the base of the tent will not be covered with ​canvas.)
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20. Q180
    From a solid ​cylinder whose height is $2.4$ cm and diameter $1.4$ ​cm, ​a conical cavity of ​the same height and same ​diameter is hollowed out. Find ​the total surface ​area of the remaining solid to the nearest cm${}^2$.
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