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_txspiSruGsj-OIjOnhafkz6I6ctaNZj2AHlzYFhklpKfa4NLd69aheJyamrXL3Z94vGAN1iqgQQTsPfu8YLC68sG1H2ztPv4uxsV4abLgfiv0KM5RwKpyRWlMUPplyVOMbs627nkfrKwxOgIpSm9NkPYH6vw=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_sIWzjcFgkdz7qVdSOmpjmtkIjbCC-P3iR3yaXnds5Jurzy8Zg_VQrmdSe_1AO9k56XDTQEHGUeEXo4QLZsn8JR_nQnq4_H1AgsvJZol-3oLAzpzUgsSWvwb-RLAuo4Uc3SNrsQ5OhDVHtecOpXEToFK98TLg=s0-d)
Question 4
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tfpC44k5SWGPqUWiF6pGJj7LM7BeUKKh8tG4UE5G2yftfQ8YyAf3yQ94a9q51oxL8ew-_ItojIredLAjbkPfBnP4F0xc9PXTCGacTo65godkCOkuLsOIPESv0229CZ30rrqgiXju276-miBVH3UCqkIfozJA=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_sWG4PvklV4_DtF09AYno3_cq1RAi0ry8p24KSIv49eMR-kHVnpOSlB5PLOhBMUTnc9rI6sWoBGEyM-cZ3uZuSt1S0YK5YyXRLK77xrlfrDc0rVmImIyVM1D01QEH-iic9nlvz56iigrE6W7vJ8R8yPjBvAtjY=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_sBJzlBNHjYbNcqm7ij2InDie6e4Z4flHDQYcQhDxU8kw4rBW5eaZHhkbZJ2WbUUMw6mhq76Y98HMILvOE61W89M13OyzM5Rysrwacnk_HORswucXfE8a1aiioypfUExFMlBsL-V26h4F1v8idk3Os6YM_ZE_I=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_uZalY_WwhtT8YnY5W9S304Q7m-3lyX2zH2C_kyfI3im9knUfUOK5A-fNzFf32U5yFiC3XWEFh4WtnxxBqEHqwJqybPqMg0qGeqVgkL8mPT5pNAqEehqr4NsKKMHg4elw13f2S7oLwGNjmLRn6XPcBwW-jqCXM=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_vT3PJt2RJegpFRgtsheRBeuNuVP8mkaxENfDDs4rikJbU1r7SGynzt41B5yOQMibq0pvMI5Gxq8XFepGgNYeG68e1lj0au8JH8oYPLOxGUlKMzJFXV1l0LUHyBPqaKwGhCNC9wyZWjEDsV6IQfdQhvL5xMTpg=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.