# mathematics ii sem

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http://www.cbseguess.co m/Guess Paper 2011 Class IX Subject Mathematics 1. Surface Area and Volumes 2. Statistics3. Probability

15 10 06 14 10 10 10 05

4. Linear Equation in Two Variables5. Quadrilaterals

6. Area of Parallelogram and Triangle7. Circles 8. Constructions

General Instructions: (i) (ii) All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A comprises of10 questions of 1mark each, Section B comprises of 8 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each. (iii) Question numbers 1 to 10in section A are multiple choice question where you are to select one correct option out of the given hour. (iv) There is no overall choice. However, internal choice has been provided in 1questionof 2 marks, 3 questions of 3 marks each and 2 questions of 4 mark each. You have to attempt only one of the alternatives n all such question. Use of calculator is not permitted CONTAINS

Surface Area and Volumes Statistics Probability

3-9 10-12 13-15

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Linear Equation in Two Variables Quadrilaterals Area of Parallelogram and Triangle Circles Constructions

16 17-19 20-21 22-23 24

SURFACE AREA & VOLUME Surface Area of Cuboids. Surface Area of a Cube. Surface Area of a Right Circular Cylinder. Surface Area of a Right Circular Cone. Surface Area of a Sphere/ Hemisphere. Volume of Cuboids. Volume of a Cube. Volume of a Cylinder. Volume of a Right Circular Cone. Volume of a Sphere/ Hemisphere

Units of Measurement of Area and Volume Length: 1 Centimetre (cm) 1 Decimetre(dm) =10 milimetre(mm) = 10 Centimetre.

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http://www.cbseguess.co m/1 Metre 1Decametre (dam) 1 Hectometre (hm) 1 kilomemetre (km) 1 Myriametre Area: 1cm2 =1cmX1cm= 10mmX10mm=100mm2 1dm2 =1dmX1dm=10cmX10cm=100cm2 1m2 =1mX1m=10dm=10dm=100dm2 1dam2 or 1are = 1damX1dam=10mX10m=100m2 1hm2=1hectare= 1hmX1hm=100mX100m=10000m2=100dm2 1km2=1kmX1km=10hmX10hm=100hm2 or 100hectare

=10dm =100cm =1000mm. = 10m =1000cm.

= 10dam =100m. =1000m =100dam =10hm. =10Kilometre.

Volume: 1cm3=1ml=1cmX1cmX1cm=10mmX10mmX10mm= 1000mm3 1Litre= 1000ml =1000cm3. 1m3=1mX1mX1m=100cmX100cmX100cm=106cm3=1000litre=1kilolitre 1dm3=1000cm3 1m3=1000dm3 1km3=109m3

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Surface Area and Volumes of Cuboids. Let there be cuboids of Length (l), Breadth (b), Height (h), Area (A) and Volume (V):1. Total surface area of the cuboids = 2(lb+bh+lh).2. Lateral surface area of the cuboids= 2(l+b)h,

i.e. Product of (Perimeter of the base) and (Height).3. Diagonal of the cuboids= l2+b2+h2 i.e. square root of (l2+b2+h2).

4. Length of all 12 edges of the cuboids= 4(l+b+h).5. Volume of a cuboids (V) =lbh, i.e. Product of (Area of the base) and (Height)

6. l=V/bh; b=V/lh; h=V/lb or height = Volume divide by area of the base.

Surface Area and Volumes of a Cube. If the length (l) of each edge, Area (A) and Volume (V) of a Cube:1. Total surface area of the cube=6l2 2. Lateral surface area of the cube=4l2 3. Diagonal of the cube =3l i.e. cube roots of length.

4. Length of all 12 edges of the cube=12l.5. Volume of a Cube (V) = l3= (edge)3. 6. Edge of a cube= Cube roots of cube i.e.

(edge).

Surface Area and Volumes of a Right Circular Cylinder.o

Radius: The radius (r) of the circular base is called the radius of the cylinder.

o Height: The length of the axis of the cylinder is called the height (h) of the cylinder.------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com

http://www.cbseguess.co m/o Lateral Surface: The curved surface joining the two base of a right circular cylinder is called Lateral Surface. o Hollow Cylinder: A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder.

Radius (r), height (h), Area (A), and Volume (V) ; 1. Lateral or Curved surface area= 2 rh =Product of Circumference of the circle and height2. Each Surface area= r2 3. Total surface area of Right Circular cylinder= (2 rh+2 r2) = 2 r (h+r). 4. Each Base surface area = (R2-r2) {R= radius of outer cylinder, r=radius of

inner cylinder). 5. Lateral or Curved surface area of hollow cylinder= (External surface area) + (Internal surface area) = 2 Rh+2 rh=2 h(R+r).6. Total surface area of hollow cylinder=2 Rh+2 rh=2 (R2-r2)

=2 h(R+r)+2 (R+r)(R-r) =2 (R+r)(h+R-r) 7. Volume of the cylinder =Measure of the space occupied by the cylinder=Product of the area of each circular sheet and height= r2h. 8. Volume of a Hollow Cylinder = Exterior Volume Interior Volume = R2h- r2h= (R2-r2)h Surface Area and Volumes of a Right Circular Cone.o

Base: a right circular cone has a plane end, which is in circular shape. This is called the base ( r2) of the cone. Height: The length of the line segment joining the vertex to the centre of base is called the height (h) of the cone.

o

http://www.cbseguess.co m/o Slant Height: The length of the segment joining the vertex to any point on the circular edge of the base is called the slant height (l) of the cone. o Radius: The radius of the base circle is called the radius (r) of the cone. o The curved surface area of a cone is also called the lateral surface area. A Hollow Right Circular Cone of radius (r), height (h) and slant height (l), Area (A), Volume (V) then: 1. Length of the circular edge=2 r2. Area of the plane = r2

3. Curved surface area of the cone= Area of the Sector = 1|2 X (arc length)x( radius) =1|2x2rxl=rl. = Half and (product of circumference of base) and (slant height).4. Total surface area of the cone =Curved surface area + Area of the base.

= rl+ r2= r (l+r).5. Volumes of a Right Circular Cone=3(Volume of the cone of radius r and height) =

r2h=1/3( r2) X h= 1/3 X (Area of the base) X (height).

Surface Area and Volumes of a Sphere/ Hemisphere.

o Sphere: A sphere can also be considered as a solid obtained on rotating a circle About its diameter. o Hemisphere: A plane through the centre of the sphere divides the sphere into two equal parts, each of which is called a hemisphere. o Spherical Shell: The difference of two solid concentric spheres is called a spherical shell. o A spherical shell has a finite thickness, which is the difference of the radii of the two------------------------------------------------------------------------------------------------------www.cbseguess.com Other Educational Portals www.icseguess.com | www.ignouguess.com | www.dulife.com | www.magicsense.com

http://www.cbseguess.co m/solid spheres which determine it. Sphere is the radius r, Area (A) and Volume (V);1. Surface areas of a sphere: S=4 r2. 2. Curved surface area of a hemisphere: S= 2 r2. 3. Total surface area of a hemisphere: S= 2 r2+ r2=3 r2 4. If R and r are outer and inner radii of a hemisphere shell, then Outer surface area

= 4 R2.5. Volume of a sphere V= 4/3 X ( r3). 6. Volume of a hemisphere V=2/3 X ( r3). 7. Volume

of the spherical shell whose outer and inner radii and R and r respectively, V=4/3 (R3-r3 )

Bibliography: R.D. Sharma| NCERT Text Book|

Section A1. The curved surface area of a right circular cylinder of height 14 cm is 88cm2.

Find the diameter of the base of the cylinder.

http://www.cbseguess.co m/2. Curved surface area of a right circular cylinder is 4.4m2. If the radius of the base

of the cylinder is0.7m, find its height. 3. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 21 cm. 4. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.5. Find the radius of a sphere whose surface area is 154cm2. 6. A matchbox measures 4cm x 2.5cm x 1.5cm. What will be the volume of a

packet containing 12 such boxes? 7. A cubical water tank is 6m long, 5m wide and 4.5m deep. How many liters of water can it hold? 8. The capacity of a cubical tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.3m and 10m.9. The height and the slant height of a cone are 21cm and 28 cm respectively. Find

the volume of the cone.10. If the volume of a right circular cone of height 9cm is 48 cm3, find the radius of