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Solved problems for the chapter:

Solid shapes

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Prism for KS4

1. Types of prisms

1.1. Vertical and oblique prisms

1.2. Regular prisms

1.3. Equilateral prism

2. Prism surface area

3. Prism volume

4. Forum

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Cone for KS3

1. Cone Properties

1.1. Elements of a cone

1.2. Surface of an upright cone

1.2.1. Vertical Cone Grid

1.2.2. Area of an upright cone

1.3. Volume of an upright cone

1.4. Axial section of an upright cone

2. Types of Cones

2.1. Vertical and oblique cones

2.2. Equilateral cone

3. Forum

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Surface area and volume of a pyramid

1. Pyramid Properties

1.1. Characteristic elements of the pyramid

1.2. The area of the pyramid

1.2.1. Pyramid Network

1.2.2. Calculating the area of the pyramid

1.3. Volume of an upright pyramid

2. Types of vertical pyramids

2.1. 3, 4, 5, ..., n side of the pyramid

2.2. Equilateral pyramid

2.2.1. Regular base pyramid

2.2.2. Equality of the pyramids

2.3. Special examples of pyramids

2.3.1. Properties of three-sided pyramid

2.3.2. Quadrilateral pyramid

2.3.3. A regular four-sided pyramid

3. Forum

↓ Show theory [3] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:solid_shapes/5333/

Example 1.

Circle the correct answers. The base area of a cuboid can be:

triangle
square
rectangle
rhombus

Example 2.

Draw a cuboid and mark all the edges. How many edges does a square have?

Using Pythagorean theorem, write a formula for calculating the diagonal (base plane) of a cuboid. From the formula, make the width the subject of the formula

A cuboid is sketched above, Using pythagorean theorem, write the formula for calculating the lateral face diagonal of the cuboid , also, use the formula to express the height of the cuboid .

Using Pythagorean theorem, write a formula for calculating the diagonal .

From this formula, express the length of the cuboid.

A cuboid is sketch below.

Write down the formula by which we use the Pythagorean theorem to calculate the space diagonal of a cuboid, and from it express the diagonal of the base plane as the subject of the formula.
Write a formula with which we use the Pythagorean theorem to calculate the space diagonal of a cuboid, using the length a, the width b and the height c and express the width b of the cuboid as the subject of the formula.

Draw the development of the figure below where side length of the cube is 4 cm.

Figure

Calculate the angle between the body diagonal of the cube and the side CG of the cube as shown in the figure below.

Figure

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

10.

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.

11.

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?