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mathematics UK Year 8 Mathematics (KS3)
 
Solved problems for the chapter:
 

Coordinates of the midpoint of two points

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Cone for KS3
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:coordinates_of_the_midpoint_of_two_points/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.

    
13.


Calculate the height of the cuboid above, given the diagonal of the base and the diagonal of the side.

    
14.

The side of a cube measure . Using Pythagoras' theorem, derive the equation for calculating the plane diagonal and calculate it to two decimal places.

    
15.

We have a cube with a diagonal length of . Using Pythagoras' theorem, derive the equation for calculating the length of the edge a of the cube and calculate it to two decimal places.

    
16.

The plane diagonal of a cube measures . Using Pythagoras' theorem, derive the equation for calculating the edge of the cube. Calculate the sum of all edges of the cube .

    
17.

The side of a cube measures . How many millimeters does the body diagonal measure?

    
18.

We have a cube with an edge of . Using Pythagoras' theorem, derive the equation for calculating the length of the body diagonal and calculate it.

    

19.

The body diagonal of a cube measures . Calculate the side of the cube.

    
20.

The edge of the cube has a length of . Calculate the area and perimeter of the figure .

    
21.

We have a cube with an edge of . By what percentage do the face and body diagonals increase if the edge of the cube is increased to ?

    
22.

How much does the area of a cube increases if we increase the length of the edge of by ?

    
23.

Write the components of a prism on the lines. Is a prism a 2-D or 3-D shape?


    
24.

Name the prisms in the figures.


    
25.

We need cardboard to build a triangular base prism grid. The base is an isosceles triangle with area . How much cardboard do we need to coat this prism?

    
26.

The volume of an equilateral triangular base prism is and the height is . What is the length of a side of the base of such a prism?

    
27.

The length of the side of an equilateral triangular base prism measures and the total surface area measures . Calculate the volume of the prism.

    
28.

The volume of an equilateral triangle base prism measures and the base area measures . Calculate the total surface area of the prism. The result should be accurate.

    

29.

The volume of a equilateral triangular based prism is and the height is . Calculate the curved surface area of the prism.

    
30.

The curved surface area of an triangular base equilateral prism measures . Calculate the volume of the prism.

    
31.

We need to repaint a wood to protect a wooden cube. What is the volume of the cube?

    
32.

The curved surface area of an equilateral triangle base prism measures and the height is four times the length of one side of the base. Calculate the height and volume of the prism.

    
33.

The total surface area of an equilateral triangle base prism is five times the area of its base. The curved surface area measures . Calculate the height of the prism.

    
34.

The length of one side of the base and height of an equilateral triangle base prism are in the ratio 2:3, and the curved surface area measures . Calculate the volume of the prism.

    
35.

How much area can be paved with base edge cubes cut from granite? Assume no cutting losses.