Unit-IV; Professional Sales Representative (PSR).pptx
Class9 surface areas & volumes
1. Surface Areas & Volume
Let’s define these terms
1) Cuboid: Box shaped 3D solid object with 6 flat sides. All angles are right angles & all faces
are rectangle.
2) Cube: Box shaped 3D solid objects with 6 flat side. All angles are right angles & all faces are
square. All sides are equal.
3) Sphere: Perfectly round geometrical & circular 3D object like a ball. It is set of all points that
are all at same distance from a given point (center) in a 3D space.
4) Hemisphere: It is half of sphere.
5) Cylinder: 3D surface formed by the points at a fixed distance from a given line segment
called Axis. Solid enclosed by this surface & 2 planes perpendicular to axis is called cylinder.
6) Right Circular Cylinder: Cylinder where 2 planes are circular & also these planes are
perpendicular to axis.
7) Cone: 3D object that tapers smoothly from a flat base to a point called apex or vertex. Base
need not be circular
8) Right Circular Cone: Cone with circular base & also base perpendicular to axis.
It has huge application in day to day life.
1. Surface Area is used to find costof painting a wall
2. Volume is Used to find costof building a wall
3. Surface Area is used find costof creating a box
4. Volume is used to find the weight of grains that a box can hold
5. Volume can also be used to find number of people that can stand in a room
6. Surface area conceptis required to find the cloth required to build a tent
7. Surface area conceptis also used to find costof making pencil stand
8. Volume Conceptcan be used to find number of pencils that a pencil stand can
hold
9. Volume conceptcan also be used to find the volume of water in a tank or well
2. Surface Area of a Cuboid & Cube:
1.SurfaceArea of a Cuboid = 2(lb + bh + hl)
2. SurfaceArea of a Cube = 6a2
Numerical: If a Cuboid box has length, breadth & height as 80 cm, 40 cm
and 20 cm. Find Surface Area.
Solution: l=80cm,b= 40 cm, h= 20 cm
Surface Area of a Cuboid = 2(lb + bh + hl) = 2 ( 80*40 + 40* 20 + 80 *
20) cm2 = 11200 cm2
Surface Area of a Right Circular Cylinder:
1.Curved Surface Area of a Cylinder = 2πrh
2.Total Surface Area of a Cylinder = 2πr(r + h)
Numerical: Find Curved Surface Area & Total surface area of a cylinder
of length 25 cm with a 3.5 cm radius.
Solution: Here r = 3.5 cm & h = 25 cm
Curved Surface Area of a Cylinder = 2πrh = 2 * 22/7 * 3.5 * 25 cm2 =
550 cm2
3. Total Surface Area of a Cylinder = 2πr(r + h) = 2 * 22/7 * 3.5 (3.5 + 25)
= 627 cm2
Surface Area of a Right Circular Cone:
1. Curved Surface Area of a Cone = πrl , where r is its base radius and l its slant height
2.Total Surface Area of a Cone = πr(l + r) , where r is its base radius and l its slant
height
Numerical: The height of a cone is 16 cm and its base radius is
12 cm. Find the curved surface area and the total surface area
of the cone.
Solution: here h= 16, r = 12
Curved Surface Area of a Cone = πrl = 3.14 * 12 * 20 cm2 =
753.6 cm2
Total Surface Area of a Cone = πr(l + r) = 3.14 * 12 * (20 + 12)
cm2 = 1205.76 cm2
Surface Area of a Spere:
1.Surface Area ofa Sphere = 4 π r2
, where r is the radius of the sphere.
2.Curved Surface Area ofa Hemisphere = 2πr2
, where r is the radius of the hemisphere
3.Total Surface Area ofa Hemisphere = 3πr2
, where r is the radius of the hemisphere
Numerical: Find the surface area of a sphere of radius 7 cm.
Solution: Here r = 7 cm
Surface Area of a Sphere = 4 π r2 = 4 * 22/7 * 7 * 7 cm2 = 616 cm2
Numerical: Find curved surface area & total surface area of a
hemisphere of radius 21 cm.
4. Solution: Here r = 21 cm
Curved Surface Area of a Hemi Sphere = 2 π r2 = 2* 22/7 *21 * 21
cm2 = 2772 cm2
Total Surface Area of a Hemi Sphere = 3 π r2 = 3* 22/7 *21 * 21 cm2 =
4158 cm2
Volume of a Cuboid & Cube:
1.Volume of a Cuboid = length × breadth × height
2.Volume of a Cube = edge × edge × edge = a3
Numerical: Find volume of a cube of side 3 cm
Solution: Here a= 3 cm
Volume of a Cube = a3
= 3*3*3 cm3 = 27 cm3
Numerical: Find volume of a Cuboid of side of length 3 cm, breadth 2
cm & height 4 cm.
Solution: Here l= 3 cm, b=2 cm & h= 4 cm
Volume of a Cube = l*b*h = 3*2*4 cm3 = 24 cm3
Volume of a Cylinder:
1.Volume of a Cylinder = πr2
h , where r is the radius and h is the
height of the cylinder.
Numerical: Find volume of a Cylinder of length 5 cm & radius 7 cm.
Solution: Here r= 7 cm & h= 5 cm
5. Volume of a Cylinder = πr2
h = 22/7 * 7 * 7 * 5 = 770 cm3
Volume of a Right Circular Cone:
1.Volume of a Cone = 1/3 πr2
h , where r is the base radius and h is
the height of the cone.
Numerical: Find volume of a Cone of height 6 cm & base radius 7 cm.
Solution: Here r= 7 cm, h= 6 cm
Volume of a Cone = 1/3 πr2
h = 1/3 * 22/7 * 7 * 7 * 6 cm2 = 308 cm2
Volume of a Sphere:
1.Volume of a Sphere = 4/3 πr3
, where r is the radius of sphere.
2.Volume of a Hemisphere = 2/3 π r3
, where r is the radius of the
hemisphere
Numerical: A hemisphericalbowl has a radius of 3.5 cm. What would be
the volume of water it would contain?
Solution: Here r= 3.5 cm
Volume of a Hemisphere = 2/3 π r3
= 2/3 * 22/7 * 3.5 * 3.5 * 3.5 cm3 =
89.8 cm3
Numerical: A shot-putt is a metallic sphere of radius 4.9 cm. Find the
volume of metallic shot.
Volume of a Sphere = 4/3 πr3 = 4/3 * 22/7 * 4.9 * 4.9 * 4.9 cm3 = 493
cm3
