Complex Area and Volume
Complex mensuration involves calculating areas and volumes of composite shapes and curved solids such as spheres, cones, and cylinders using their formulas.
What You Need to Know
Key Concept Diagram
Sphere: V = (4/3)pi r^3, SA = 4 pi r^2
Cone: V = (1/3)pi r^2 h, curved SA = pi r l (l = slant height)
Composite shapes: add or subtract simpler shape formulas
Always check units and convert if necessary before calculating
Key Vocabulary
Mensuration
The branch of mathematics dealing with measurement of lengths, areas, and volumes
Composite shape
A shape made up of two or more simpler shapes combined
Slant height
The distance from the apex of a cone to a point on its circular base edge
Surface area
The total area of all outer surfaces of a solid
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Find the volume of a sphere with radius 3 cm (use pi = 3.14).
Question 2
A cone has radius 4 cm and height 9 cm. Find its volume (use pi = 3.14).
Question 3
To find the area of a composite shape that is a rectangle with a semicircle on top, you should:
Key Concepts Summary
- ●Sphere: V = (4/3)pi r^3, SA = 4 pi r^2
- ●Cone: V = (1/3)pi r^2 h, curved SA = pi r l (l = slant height)
- ●Composite shapes: add or subtract simpler shape formulas
- ●Always check units and convert if necessary before calculating