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_u4CVMfeRJisVD4oqg8O8S-xU6hWnbr04peTQi-IbHd-R8idIZU1-4OPELuTTS3pawf9IX7kD9pVRZVx3NQQ1XthP7sjQnP018BJtdhkMvjI-wQCoNIAmb_dA6nrPukZCRuF6vJpzIoWmT6t1izMLUeH_Hjhw=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_vIX1ZdyTJfmF9MZZRthdh92m1-oiCJHTimY1RnhR8ejBYf5QEb9z-RG3Y7jBEW11kjmPO2hGsdQu0PmLwDHilBUEfJiwEg_rDW6Wd-t0_IRqdTO5rE0naAiS9ffPTsXERf0taLs2PtJ2H2xoFrAQmfgW5nIQ=s0-d)
Question 4
![[image]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tapbJOvM2-Nwi7nczQ-IOLispr8FXeEp8B56YxU2-6IMz7fqLEFrkRsDy4X8L2NBFPxR9qczyKPPXjeegz0u_wouEjwlObC8zYn5INIJqmXZLeYW4TWYMT-XZgv_UcAwpmm_1jjI2OEYX7VT7taOQFM6WhLg=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_v_-VPtd-4Rrw1VbFPCcbIxe-Gl0_KGa9AGHwxkAKP6KmMN9vL8bNa1Y1Y-7MBERDn6qQCZb9pUTuZRp0W1AIP4WhJef_a19t3VJwkTs2zdvGioOCcVgNY0caHfMEdi20J3748mMY0x-EGFsMRxBhxaL_WlkM0=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_sjtG7tzAdV1UUJYoAt6iFfTRdHXqb9CXyqaphrNno_3CoJxYOZ0GsMSuFeVl48TqZHpPnY5x_JBCCiPc22bCvDAru2Q0ZchZ80Bq29Kwz4CPZ4zuoO4ZTxx25im73AfDN6IpLPWZHkFHEYSVacXUgfB56-nQs=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_v-8zJKw8dlFZKOlPKZLw67lgtkrV8sQqWop0EFodPXySE74QZWK2XxHT3teB5UC2BFAdyDWlJAHehnA1U_ge3uQV5RC4cyccGZPg8yOkF4CFt97wbACP4NU23duwAtSWs9LUSrx8uKhUhsIVjdWnWroiau4e8=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_s0HkStrqJEzvHlpO0fg7xihtWYehp3z2-I5WVAr-buNw8Hw_GmapB0IxmtWvwv1XV4sA0dBvLF0nN0KWyE86rOLypdjy78TG659x41TX15cM7rqPexGowRZpCYq4lQf7ZYlW7l_ZEFjrPW__oOIzg3fsQBMIk=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.