mathematics
  Personalized »

KS3
 
 
 
Year 7
 
 
Year 8
 
 
Year 9

KS4
 
 
 
Year 10
 
 
Year 11

A-levels
 
 
 
Year 12 (AS)
 
 
Year 13 (A-levels)


physics
  Personalized »

 
 


KS4
 
 
 
KS4 Level Physics

A-levels
 
 
 
AS Level Physics
 
 
A-levels Physics


 
 
Private tutors
 
 
Find a tutor »


Login for parents »
 
 
 
Login for students »
 
 
 
Login for private tutors »
 
 
 
Login for teachers »
 


Unlock access to content
 
Select one option:



Free of charge
Unlock the chapter   "Properties of 3-Dimensional Shapes"  



Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »
Subscribe to OpenProf     If you do not get a better grade, you get your money back!
 


Unlock access to all problems solutions.
Available from 8.25 £ / month.
Continue »
mathematics UK Year 8 Mathematics (KS3)
 
Solved problems for the chapter:
 

Properties of 3-Dimensional Shapes

download pdf
View the theory »
Cone for KS3
open
View the theory »
Surface area and volume of a pyramid
open
↓   Show theory [2]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:properties_of_3-dimensional_shapes/4116/


Example 1.

Write the components of the cone labelled from a - g. Is a cone a two-dimensional or three-dimensional geometric shape?


    
Example 2.

Draw a sketch of a cuboid:

  • Write down how many vertices a cuboid has and explain how to mark them.

  • On the sketch, mark all vertices.

    
3.

  • Which figure is obtained by cutting a cone at right angles to the base, and the plane passes through the vertex?

  • Which figure is obtained by cutting through the plane in which the height of the cone lies?

    • vertical cone

    • equilateral cone

  • What do we call the figure obtained?

    
4.

Calculate the lengths of all plane diagonals and the length of the diagonal of a square with sides a = 3 cm, b = 6 cm and c = 5 cm. Round the result to one decimal place.

    
5.

The base area of a circular-based cone is and the curved surface area is . What is the total surface area of the cone?

    
6.

We need a of paper to make a cone. The base of the cone is a circle with area . What will be the area of its curved surface in decimetre square?

    
7.

The volume of a cone measures and the height . What is the radius of the cone?

    
8.

The volume of a cone measures and the base area equals . Calculate the area of the axial section of the cone.

    

9.

Write the part of the cylinder labelled with alphabets. Is the cylinder rectangular or circular?


    
10.

The volume V of a cone measures . If the height h of the cone is , calculate he diameter of the cone.

    
11.

The radius of the cone measures . What does the slant height of the cone measures if the area of the circular base and the curved surface area are in the ration ?

    
12.

A pyramid has as its base as a rectangle with an aspect ratio of . The perimeter of the base measures , and the height of the pyramid measures . Calculate its volume.