Cone, Cylinder, and Sphere

Created by:Nurina Ayuningtyas

Wahyu Fajar S.Yan Aditya P

Yola Yaneta H

hs

r

A cone has two parts, namely the base and the lateral.

h is the height of the cone, r is the radius of the base, and s is the slant height.

Lateral

Base

r

Lateral

Base

Element of Cone

s

h

r

Flat Top

Flat Base

Lateral

Flat Top

Lateral

Flat Base A cylinder has three parts, namely the flat top, flat base and the lateral. h is the height of the cylinder and r is the radius of the base.

Element of Cylinder

rpr is radius of sphere and p is point centre.

Element of Sphere

Nets of Cone

Nets of Cylinder

Find formulas of the surface area of cylinder, cone, and

sphere

Surface area of Cylinder• Look at the net of the cylinder below. The

total surface area can be found by adding all the three areas.

Total surface area = Lateral area + (2Xbase area)

)(2

22 2

rhr

rhr

Surface area of Cone• A cone has two parts, namely the base and

the lateral.

• On Figure, t is the height of the cone, r is the radius of the base, and s is the slant height.

• If the cone is cut along the slant s and its base, we will get the cone net which consists of sector which has radius s and a circle with radius r, as shown:

Surface area of Sphere

• How do you find the surface area of a sphere? • The surface area of sphere same with the

lateral of Cylinder.

Surface area of Sphere = Lateral area of cylinder= 2πrh= 2πr X 2r

S = 4πr₂

Exercise

• Determine the total surface area of this cylinder.

• Find the volume and the total surface area of each of the following cones. (π = 3.14)

Volume of Cone

Find the formula

Do you remember about the formula of pyramid?

Volume of pyramid = 1/3 x Area of Base x Height

Because the cone base is a circle with radius r, then Area of Base = π r 2

Find the formula

Actually the cone is a pyramid, because have top point. (titik

puncak) and altitude.But the cone’s base is a circle with radius r, So the Area of Circle = π r 2 (base of cone)

Find the formula

From this process so the volume of cone is same as volume of

pyramid.

Volume of cone = 1/3 Area of Base x Height = 1/3 x π r 2 x h

Therefore the Volume of Cone = 1/3 π r 2 h

Volume of Cylinder

Volume of Cylinder

Actually the cylinder is a prism, because the base and top side are parallel and congruent. But the cylinder have base a circle

Let’s we see this pictures

So the volume of prism = volume of cylinder

Can you compare them ?

Volume of Cylinder =

Volume of Prism =

Hence the volume of cylinder = π r 2 x h

Area of Base x Height

= r.r x h

=

Area of Base x Height

π r 2 x h

Because the cylinder’s base is a circle so the base area is r.r

Volume of Sphere

r

r

Find the Volume of Sphere

Prepare the instrument and materials : Scissor, Cutter,

Rice, Plastic ball

1. Cut the ball become 2 parts

4. Repeat until all of hemisphere is full flat. And note it.

3. Fill the cone by rice until full flat. And pour to the one of hemisphere

2. Make a cone by the height and the radius same with radius of ball

The ways...........

Volume of Sphere

Height of cone = radius of sphere = r

Volume of Sphere

From theis activity we see that volume of rice that

poured to hemisphere is not change.

It means that the volume of hemisphere = 2 times of

coneVolume of cone = 1/3 π r 2 h (h=r)

= 1/3 π r 2 rVolume of hemisphere = 2 x 1/3 π r 2 r so

Volume of Sphere = 4 x 1/3 π r 2 r

= 4/3 π r 3

Design The Cone Picture

1. Make an ellipse

2. Find and mark the centre

point of ellipse

3. Make an altitude

4. Mark this end point of

altitude by O.

5. Connect the O lie ellipse

r

o

Design The Cylinder Picture

1. Make an ellipse

2. Make parallel line that lie

side of ellipse

3. Make ellipse once again to

upward.

Design The Sphere Picture

1. Make an circle

2. Find and mark the centre

point of circle.

3. Make ellipse from centre

point of circle