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_ukUFLV7yr9yhdk6F7i3k5XI7hhuBKA-p-8TiFpSvF3n5OyNRxpnaRI0Pzy6WvT92m824DL7bdBy9NyliL1Cz25q_H4UtpNDsuxHu5IaJni1WSJKa98Ipwofg21vGRu6dY7qua6-054GRtzJ0_EmvFPi-6vXg=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_u_0F-TTbe_LYcLqpVtWpdJs8W6wBQQVNRRRhKbjd48crFho5ZyOANKHy8znT98QmiicWo_RxJwCqy8pk6bpJ1V0w9xq_LNCDxwsVCP98Wp2461hMhe3Fv7ZcvHLlrAORK9Bfd0shzIviYkn99lvmRQ7vqmQQ=s0-d)
Question 4
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uK_daNeN9KoBOSjV2rjfI09aAnXjkkrEwaZcm_OXUJh58ZrPqHIUiholoVhbyxEYD4Lrup4ihyoeVVYJ0QAl7EF0kalYAL3xuuDqeGYSgkLpsE1vKD1spSiMgHKXOSjgaJ6AL09CuYh-h9qH_F-T8G8M3kwA=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_t9PebG27RUpQcEcrgnS_yjcrnN4LbmZWaUyTI0d59rmkoG5cHOvF-oalDx31DG9a_2cPnkN4BewGF02mXuUejVL7wXFUG89G_lYI07XB6qmJvzFtO3_1-CvKF4M9gjvSTliKMg5TgtTvgUJVP9edfv8gDsraU=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_ugorDuPOohMXlKCGsZ9yQoDY56Ed4PdfvN4W6Yct6aI-m8iwDF5NWy3JQex2ILJijsRbJn3nOHACnnjWU0ELW6LLjnm9MUv8jJ6e_uGo0mv0R4yV_dzDA6G73YKYSCRnW0wxNKEpf9bwkhd66FYOIhPvJFyuM=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_sgEyA_FtV4mA7o5P8n2agjq4br-A_TkHsN6iNCSIz4EXO4m9eqbgcHqBcuiM2zSNAqVcpYY1pEtkxEIJXCIqgKOLUa6vazKPYuuA6YZJ_xy8VPol2FH2vdSk-NXyejk3iu24ppcnn0FrpFziYnv-PBwvvPTOo=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_sivSbR6qgUrr1y2KaypgvPWa3DQCgDkdydrTDhWJxiGSeK0lYuvTc9tgpG5wEaavXxvPntdyFfYJH1HDWErRTrTtp1JTz-DRujbq8mBoMgm9-s8OHFDP4r2dtlQFL2_Xe2858zEVMTj0IQld4WE-5VDC6Qlbg=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.