Cylinder Cone Sphere

A solid shape with one curved surface and two circular bases.

Parts of a Cylinderbase radius

The radius of the cylinder is the radius of the base. The height of the cylinder is the perpendicular distance between the bases.

Lateral surface

Height h

base

Surface area of solid figure Nets of cylinder

2 .r

How to find the surface area of a cylinder? Surface area = 2 (area of base) + (area base) (circumference of base) (height) Symbols S = 2 B + Ch =2 B= C=2 r + 2 r h r rr h

4 ft.

Find the surface area of the cylinder. Round your answer to the nearest whole number. Solution:3 ft.

S= 2 =2 = 18

r + 2 r h (3) + 2 + 24 (3)(4)

= 42 = 132The surface area is about 132 square feet.

Practice ProblemsFind surface area of the following cylinders. Round answer to nearest whole number 1.

2. 3 in.

3. 2m 1m 5 in.

12 ft.

10 ft.

Volume of Cylinder Vcylinder = Vprism

So, the V = base x height= r2 xtr

h

Problem Example..y It has a height of 6cm . y What is the size of the radius ?6cm

2cmy Calculate the volume:

V=

r2x

h4cm

V = 3.14 x 2 x 2 x 6 V = 12.56 x 6 V = 75.36 cm3

then, what about

?

A solid shape with a circular base and a curved surface that tapers to a point.

Slant height (l) Height (h)

Diameter (d)

Radius (r)

Surface area of conel

2r l

l

Area of a circle having sector (circumference) 2 l = Area of circle having circumference 1 = l 2/ 2 So area of sector having sector 2 r = ( l 2/ 2 l l )x 2

l2

2r rl

r=

Surface Area of a ConeFind the area of a cone with a radius r=3 m and height h=4 m.r = the radius h = the height l = the slant height

Use the Pythagorean Theorem to find l

Surface Area of a Cone

= Tr2 + Trl = 3.14(3)2 + 3.14(3)(5) = 75.36 m2

l 2 = r2 + h2 l 2= (3)2 + (4)2 l 2= 25 l=5

V l C

f

Click to See the experiment

h

H r t rtic l i r di s f cyli d r & c s . l fc = r2 ) r2 l

t r

d

h

r 3( f cyli d r 3( V ) V 1/3

r

if both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone ,

Volume = 3V

Volume=V

+

+

=

3( volume of cone) = volume of cylinder 3( V ) V = 1/3 = r2h r2h

Mr. Mohan has only a little jar of juice he wants to distribute it to his three friends. This time he choose the cone shaped glass so that quantity of juice seem to appreciable.

y

A three dimensional solid that is completely round.

The Sphere Surface Area: A = 4 r2 Volume: V = 4 r3 /3 r

Click to See the experiment

Volume of a Sphere

h=r r Here the vertical height and radius of cone are same as radius of sphere. r 4( volume of cone) = volume of Sphere 4( 1/3r2h ) = 4( 1/3 r3 ) = V V = 4/3 r3

WHAT 3 DIMENSIONAL OBJECT IS COMPLETELY ROUND??

(CHOOSE THE ANSWER)

A cube A cylinder A pyramid A sphere

WRONG!!!

Please go back and read through the two slides titled, Types of 3 Dimensional Shapes very carefully!

YOURE CORRECT!!

Great Job! Youre very smart!