maths 10 project

8/10/2019 Maths 10 Project

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In this chapter, we shall remindourselves the formulae related to

surface areas and volume of solidssuch as cuboid, cube, right circularcone, sphere, etc.


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Dimenctions of cuboid

l: lenth of cuboid b: breadth of cuboid H: height of cuboid Total S.A. = 2(lb+bh+hl) Lateral S.A.= 2(bh+hl)

= 2(l+b)xh Volume =lxbxh


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L:lengthof an edge. Total S.A. = 6l Lateral S.A. = 4l Volume = l


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r: radius of the base h: height (or length)

Area of base = r Curved S.A. = 2 rh Total S.A. = 2 r 2 h = 2 r(r h)

Volume = rh


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r: internal radius R: external radius h: height

Area of base = (R -r) Cuved S.A. = 2(R r)h Total S.A. = 2(R r)(h R -r) Volume of material = (R -

r)h


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r:radius of base h: height l: slant hight Area of base = r Curved S.A.= 2rl Total S.A.= r rl = r(r l) Volume = rh


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r: radiusSurface area = 4r

Volume = 4/3r


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Curved S.A. of hemisphere = 2r Total S.A. of hemisphere = 3r Volume of hemisphere = r


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h= height l= slant height R= radius of base 1

r= radius of base 2 V=h(R r Rr) V=h/3,A A AA-

I= h+(R-r) C.S.=l(R r) T.S.= l(R r)R r


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1. Three cubes each of sides 5cm are joined end to end. Find the surface area ofthe resulting cuboid .

Solution. resulting solid take the shape of a rectangular cuboid having dimentions

15cmx5cmx5cm

Thus, the surface area of cuboid = 2(lb+bh+hl) = 2(15x5+5x5+5x15) = 2(75+25+75) = 350cm

2 A ll h di t i 7 h b d 22 5 d d th th d t


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2. A well, whose diameter is 7cm, has been dug 22.5cm deep and the earth dug outis used to form an embankment 10.5cm wide around it. Find the height of theembankment.

Solution. Radius of the well = 7/2m

And depth of the well = 22.5m Therefore, the volume of the earth dug out is V = (7/2)x45/2 Now, the inner radius (r) of the embankment =3.5m and the outer radius (r) of the embankment

= 3.5m+10.5m =14m Let the height of the embankment be h meter. The volume of the earth used for embankment is, V =(area of the base of the embankment)

= (R-r)xh = (R r)(R-r)h = (14 3.5)(14 -3.5)hm = (17.5)(10.5)h

Si l f th th d l f th th d g t th f 2 1


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Since, volume of the earth used = volume of the earth dug out, therefore,v2=v1 =(17.5)(10.5)h = (7/2)2(45/2) =35/2x21/2xh =45/5x3x2 =3/2 h=1.5

Hence, the height of the embankment =1.5m

3 A toy is in the form of a cone mounted on a hemisphere with the same radius The


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3. A toy is in the form of a cone mounted on a hemisphere with the same radius. Thediameter of the conical portion is 6cm and its height is 4cm. Determine thesurface area and the volume of the toy. (take =3.14)

Solution. For the conical portion, radius r = 3cm height h =4cm The slant height, l = 5cm The radius of the sphere is same as that of the cone i.e., r = 3cm Now, surface area of the toy =curved surface of the hemispherical portion + curved surface of the conical portion =2 r rl

= *2x(3) (3)(5)+ = *18 15+ = 3.14 x33 cm2 =103.62 cm2


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The volume of the toy = the volume of the hemispherical portion +the volume of the conical portion

=2/3r 1/3 rh =2/3(3) 1/3(3) cm =,18 12)cm =3.14x30 cm

=94.2 cm


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1. If the volume of a cube is 1728 cm, the length of the edge is equal to(a) 12 cm (b) 14 cm(c)16 cm (d) 24 cm

2. Two cubes each of 10cm edge are joined end to end. The surface area of theresulting cuboid is(a)1200 cm (b)1000 cm(c)800 cm (d)1400 cm

3. A rectangular t of paper 44 cmx18 cm is rolled along its length and a cylinder isformed. The volume of the cylinder so formed is equal to (take =22/7) (a)2771 cm (b)2506 cm(c) 2460 cm (d)2672 cm

4. If the radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm,then its radius is equal to (take =22/7) (a)6 cm (b)7cm(c)5 cm (d)10 cm

5 If the curved surface area of a solid right circular cylinder of hight h and


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5. If the curved surface area of a solid right circular cylinder of hight h andradius r is one third of its total surface area, then(a)h=1/3r (b)h=1/2r(c)h=r (d)h=2r

6. A hollow cylindrical pipe is 21 cm long. If its outer and inner diameter are10 cm and 6 cm respectively,then the volume of the metal used is makingthe pipe is (take = 22/7)(a)1048 cm (b)1056 cm(c)1060 cm (d)1064 cm

7. If the radius and sland hight of the cone are in the ratio 4:7 and its curvedsurface area is 792 cm, then its radius is (take = 22/7)(a)10 cm (b)8 cm(c)12 cm (d)9 cm

8. If the radius of the base and the height of a right circular cone arerespectibely 21 cm and 28 cm, then the curved surface area of the cone is(take =22/7)(a)3696 cm (b)2310 cm(c)2550 cm (d)2410 cm

9. A conical tent with base-radius 7 cm and heidht 24m is made from 5cm


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9. A conical tent with base radius 7 cm and heidht 24m is made from 5cmwide canvas. The length of the canvas used is (take =22/7)(a)100 m (b)105 cm(c)110 cm (d)115 cm

10.The total surface area of a solid hemisphere of radius 3.5 m is covered withcanvas at the rate of Rs.20 per m. the total cost to cover the hemisphere is(take =22/7)(a)Rs.2210 (b)Rs.2310(c)Rs.2320 (d)Rs.2420

11. If the volume of a vessel in theform of a right circual cylinder is 448 cmand its height is 7cm, then the curved surface area of the cylinder is(a)224 cm (b)212cm (c)112 cm (d)none of these

12. If the curved surface area of a right circular cone is 12320 cm and itsbase-radius is 56 cm, then its height is (take =22/7)(a)42 cm (b)36 cm(c)48 cm (d)50 cm

13. If a solid metallic sphere of radius 8 cm is melted and recasted into n


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13. If a solid metallic sphere of radius 8 cm is melted and recasted into nsphere solid balls of radius 1 cm, then n=(a)500 m (b)510 cm(c)512 cm (d)516 cm

14. If the diameter of a metallic sphere is 6 cm, it is melted and a wire ofdiameter 0.2 cm is drawn, then the length of the wire made shall be(a)24 m (b)28 cm(c)32 m (d)36 cm

15. If n coins each of diameter 1.5 cm and thickness 0.2 cm and melted and aright circular cylinder of height 10 cm and diameter 4.5 cm is made, then n=(a)336 (b)450(c)512 (d)545

16. If the curved surface area of a right circular cone is 12320 cm and itsbase-radius is 56 cm, then its height is (take =22/7)(a)42 cm (b)36 cm(c)48 cm (d)50 cm


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Answers 1.(a) 2.(b) 3.(a) 4.(a) 5.(b) 6.(b) 7.(c) 8.(b) 9.(c) 10.(b) 11.(c) 12.(a)13.(c) 14.(d) 15.(b) 16. (a)


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Q.1. Find the surface area of the interior four walls of the length 8 cm, breath 5 Cmand height 3.5 cm.

Q.2. Find the curved surface area of right circular cylinder of radius 8 cm and height10.5 cm. (Use = 22/7)

Q.3. Find the volume of a right circular cylinder having of radius 7 cm and height104/7 cm. (Use =22/7)

Q.4. Find the radius of the right circular cylinder of height 20 cm and volume 1571.5

cm3. (Use =22/7)Q.5. Find the radius of a sphere whose volume is 905.184 cm. (Use = 3.24)Q.6. Find the radius of a sphere whose surface area is 616 cm. (Use =22/7) Q.7. Find the curved surface area of a right circular cone having radius of its base 6

cm and vertical height 8 cm.Q.8. Find the volume of a right circular cone having radius of its base 3.5 cm and

vertical height 21 cm. (Use =22/7)Q.9. If the radii of the circular ends of a frustum of a cone of height 16 cm are 25 cm

and 13 cm respectively, find the sland height of the frustum.

Q 10 Wite the formula for finding the curved surface area of the frustum of a cone


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Q.10. Wite the formula for finding the curved surface area of the frustum of a conehaving sland height l and the radii of its circular ends as R and r.Q.11. Find the curved surface area of a right circular cone whose radius is 5 cm andvertical height is 15 cm.Q.12. (Alternate) A Solid right circular cone of diameter 14 cm and height 8 cm ismelted to form a hollow sphere. If the external diameter of the sphere is 10 cm, findthe internal diameter of the sphere.Q.13. (Alternate) water flow out through a circular pipe whose internal radius is 1 cm,at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose baseis 40 cm. by how much will the level of water rise in the tank in half a hour?Q.14. A Solid right circular cone of diameter 20 cm and height 10 cm is melted toform a hollow sphere. If the external diameter of the sphere is 30 cm, prove that theinternal diameter is 10x17/5 cm.Q.15. A well, whose diameter is 8cm, has been dug 22cm deep and the earth dug outis used to form an embankment 10cm wide around it. Find the height of the

embankment.Q.16. (Alternate) A Solid right circular cone of diameter 13cm and height 8 cm ismelted to form a hollow sphere. If the external diameter of the sphere is 11 cm, findthe internal diameter of the sphere.


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