Solid Geometry is the geometry of three-dimensional space, the kind of space we live in ...
Three Dimensions
It is called three-dimensional, or 3D because
there are three dimensions:width, depth and height
Cube (Hexahedron)
- It has 6 Faces
- Each face has 4 edges, and is actually a square
- It has 12 Edges
- t has 8 Vertices (corner points)
- Surface Area = 6 × (Edge Length)2
- Volume = (Edge Length)3
Cylinder
- It has a flat base and a flat top
- The base is the same as the top, and also in-between
- It has one curved side
- Surface Area = 2 × π × r × (r+h)
- Volume = π × r2 × h
Cone
- It has a flat base
- It has one curved side
- Surface Area of Base = π × r
- Surface Area of Side = π × r × s
- Volume = π × r2 × (h/3)
Sphere
- It is perfectly symmetrical
- It has no edges or vertices (corners
- All points on the surface are the same distance from the center
- Surface Area = 4 × π × r2
- Volume = (4/3) × π × r3
YOUR TURN :
Question 1
What is the volume of a cube of edge length 4 cm?
Question 2
A cube has edge length 5 cm
What is its surface area?
Question 3
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_udHhwdqymmApJlFZgkGXk0xzHyU590MhJzvsSPtbbmpXTHohOqqU_iC6V_km-_0sOYWRBymxttaq9Dg0BZ3YvLKX6tjSIStWN5uOuEsoXlnYgGUEdcWFvZhUJ7T3BQUzIoJshWppgoEOPxdwmcBFStU2xvvw=s0-d)
The diagram shows a cylinder of height 10 inches and radius 7 inches. What is its volume?
![math [image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s-o5Yd_DUtP2jeZglfUBfOkTgRku19e4X2uY9kJqFjK0U2RRMEe24PJuC9MfKqcVINEnJMGahTGZRPxl38N8ioH9A50ZhpYj8X4hDhL7ddM4Fb_C648MP0cZ8CMYQVchSyn85li20oGexvHvAikStR1MSIMw=s0-d)
Question 4
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_scsRJVVD54BpfpDR_8llqNmPHRYfCS_2mxyccnTt6vqiWEmnVWv2SNW5cJoKhC0C7zWG2l8RQcKeM8V2Q9LfNYNJL3ZoJoRNU2OpKI4a7qRy694Hbs97XZFNHZjxb68dSC-Lrw0fqVThs_2Lyz2pnRr2OfxQ=s0-d)
An ice cream cone has vertical height 6 in and the diameter of its top is 3.5 in.
How many fluid ounces of ice cream does it hold when filled level with the top?
Question 5
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tdqJ0BS2N8-WMcKJgI8F1kntQBFnkhD4acQiGNuiqNo-sPYvGhkFK9IHO2eNazbov4KyXAhIQ_L3pecliJGJcN-KD1994AjIez9kE47ccR1oi9aldW9Fc8a9S_vBa-6EMNbRZHP2TfeNNfZNJyLJ_26CKHfz4=s0-d)
The diagram shows a cone of height 5 cm and base radius 12 cm.
What is the total surface area of side and base?
Use
π = 3.14
Question 6
What is the volume of a sphere of radius 6 inches?
Question 7
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_silXpac1P3jHi9VBDmpHy9Hbj0Dk4GT76vyA-UuDmxShNe5D5mGhSi7M2Rh1MnFO54cOlZOhEKAqAdqInCBPLYrgf_4hI7Y-QrgEmxciWAWZsCYLVyXD0ipAoPKbuxVtd3EALwnMwtKA6QnzVc1YvzhPgENTY=s0-d)
The diagram shows the cross section of a rubber soccer ball of outside diameter 22 cm. The thickness of the rubber is 0.5 cm
What is the volume of the rubber to the nearest cm
3?
Question 8
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sX5dB-hGUoPoCdHSEj2cHdzQ_Ed36ZHQVPIk9GSGKgiVuR83pXjp-AwDQqy4f6V3K_gtWhrEJcVolJ95zm4DBeGSqbLFoQo1roRjM9T2cNqDOG7N8K3HSYCnXW84rQ8Ic4Qbswh0pr9vZoyw5Qk3pepeJgzXY=s0-d)
The diagram shows a cylinder of height 6 cm and radius 6 cm. What is its volume?
Use
π = 3.14
Question 9
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uawnN4Ho3RacQcaCW0imbKwkM8bkeOsdtxbSa9lHFKoBUaE6ihs_rHEFEUXVqyTJbmhRCdlwkRRTrMVvd_xuWtDBAIpHtf2XT1Lj8NE6wZXOQ6t1k9reLWm1_n4gB1KKFPk3aBc9stAglg0zX80ToCVu_mDwE=s0-d)
The diagram shows a cylindrical water tank of diameter 14 ft and height 8 ft
How many gallons (US liq) of water does the tank hold when full?
Use
π = 22/7
To convert from ft
3 to gallons (US liq) use the Unit Conversion Tool
at http://www.mathsisfun.com/unit-conversion-tool.php
Question 10
The volumes of the cube and the cone are equal. Express h in terms of r.