Cone, Cylinder, and Sphere Created by: Nurina Ayuningtyas Wahyu Fajar S. Yan Aditya P Yola Yaneta H
A cone has two parts, namely the baseand the lateral. h is the height of the cone, r is theradius of the base, and s is the slantheight.
A cylinder has three parts, namely the flat top, flatbase and the lateral.h is the height of the cylinder and r is the radius ofthe base.
r is radius of sphere and p is pointcentre.
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 2 rh 2 r 2 r (h r)
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 formulaDo you remember about the formula of pyramid?Volume of pyramid = 1/3 x Area of Base x Height
Find the formulaActually the cone is a pyramid, because have top point. (titikpuncak) 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 formulaFrom this process so the volume of cone is same as volume ofpyramid.Volume of cone = 1/3 Area of Base x Height = 1/3 x π r 2 x hTherefore the Volume of Cone = 1/3 π r 2 h
Volume of Cylinder
Volume of Cylinder Let’s we see this pictures Can you compare them ? Actually the cylinder is a prism, because the base and top side are parallel and congruent. But the cylinder have base a circle So the volume of prism = volume of cylinder
Volume of Prism = Area of Base x HeightVolume of Cylinder = Area of Base x HeightBecause the cylinder’s base is a circle so thebase area is r.r = r.r x h = π r 2x h Hence the volume of cylinder = π r 2 x h
Volume of Sphere r r
Find the Volume of SpherePrepare the instrument and materials : Scissor, Cutter,Rice, Plastic ball The ways...........1. Cut the ball become 2 parts2. Make a cone by the height and the radius same with radius of ball3. Fill the cone by rice until full flat. And pour to the one of hemisphere4. Repeat until all of hemisphere is full flat. And note it.
Volume of SphereHeight of cone = radius of sphere = r
Volume of SphereFrom theis activity we see that volume of rice thatpoured to hemisphere is not change.It means that the volume of hemisphere = 2 times ofVolume of cone = 1/3 π r 2 hcone (h=r) = 1/3 π r 2 rVolume of hemisphere = 2 x 1/3 π r 2 r soVolume of Sphere = 4 x 1/3 π r 2 r = 4/3 π r 3
Design The Cone Pictureo 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
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