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_sUPlD0zynOhsomP1vnxnVwYcoY3lbPRDHMn5VsxC3dxlLhGu0g6gZi6RpG69st1jytYG3B9UJ-1i8374qZ3q7C__9hK7TVsJY_tcikCx3DgFA-EOub3DetKc5PwcZHZyIfGjyPq0hCbprVY5Ra8vhW3iICVA=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_s0E1oMhQyynsk99DJo9m5fkF3nrv2xqJEntAsLx6HpTw0MGVlGKz1t2nLyeBbjkh_bM0OP0-xz0XNQOY1NMrcz5a2urURGzpvR2sB-vNbIZ5AMhKn1sUtsFba48PH55h6ftLtyV8xzqkLVrphVpOQQM1mCBA=s0-d)
Question 4
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v-KxCxN-g5SrHamDyKZeYHYnlxQvoE_Ju_hGWOnBS9liwjuCFs3UqTemDHDRU4ALIEnVAj3P3pxT3nmhePTanzp204_Io8QrhKgv4fBgO4jrZ4EHkc0Zo8ndhQlYJSH20jyE5nnMEC0m67bI7RJ4qPWX-YgA=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_vD4bPQ33gViDWS4B6LGbrthFrlqpJIaQ7EHBejCN-yoH1dvaoJuh5dLhqpDto7MLSyP6muysJUFngYbsxCP1WhLv9lkt7b_htsszHnxh4WAqZcsw3Tu-sTLBSIfhBW4HYbeIrHPgsoClPbBSZTN1SqgVgBF0s=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_sKuIxL9wrPsdZmAxv7tFXzQZp_Gamkn2G6QLuL8kvbv9LlNHj9nas6-v5_ssWFvtS9GqZdKganTeMwwpqeIgHRTzPdetQgmaK7_n0i79piHbiar7e9RwtmDhghB0m7uCyPYIvhodF_bmYZ9QOEbGQFu8uGUQI=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_sEGFO7jMlo6pqnVJ0AC9csDREDEcX-I2ZRr1A27GFxGASZ2WHejeDcUtg4DuUYAlR80iF_FdwIdF11aVOn0j1Bo4c37oNjdRrUV3vZ-ZAh6MtW0G6WdedLu0PwU9fx2aIViNSGKnM0F3TxkBNPOm4brD85Jqw=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_v3sJTFIqtQRLaRBexFlAiw-twTHHXFHbx8TDQardaRKNyCI61TV2RNpAb7LEp6hV8Ey2MvCqXOBRb7mrG5z8IOVv7VQRZPZ36A7SYuEeCysOdifxz1U4ktq-jiPJBwQmQ855ZqoBzX1fWxqwrhPUeR8xwNqX8=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.