The space occupied by the three-dimensional object is measured in terms of the volume of that object. The volume of a solid shape is the product of three dimensions, so the volume is expressed in cubic units.
Suppose the volume of a cube is measured by the product of its length, width, and height. The interior of a hollow object can be filled with air or some liquid that takes the shape of the object.
In such cases, the volume of the substance that the interior of the object can accommodate is called the capacity of the hollow object. Thus we may say that the volume of an object is the measure of the space it occupies and the capacity of an object is the volume of the substance its interior can accommodate. Area vs Volume Definition. The area refers to the region covered by the object.
And volume refers to the quantity or capacity of the object. An area is a two-dimensional object whereas volume is a three-dimensional object. The area is a plain figure while volume is a solid figure. The area covers the outer space and volume covers the inner capacity. The area is measured in square units and volume is measured in cubic units. Generally, the area is calculated for two-dimensional objects, while volume is calculated for three-dimensional objects.
Here is the pictorial representation of area and volume which shows the relation between area and volume. Let us try to understand the relation between area and volume and the difference between area and volume in detail.
For example, if a rectangle has a width of 5cm and a length of 3cm, its area would be:. Other examples of cubic units include: millimetres cubed mm3 and centimetres cubed cm3. Key Concepts In the new linear GCSE Maths paper, you will be required to solve various mathematical problems involving perimeter, area and volume. The specific questions you will be expected to answer will vary depending upon which examination board with which you are registered, but as a rule you will be required to: Calculate the perimeter of various shapes Calculate the area of various shapes Calculate the volume of various shapes Listed below are a series of summaries and worked examples to help you solidify your knowledge about perimeter, area and volume.
Worked Examples 1 — Calculating the area of a trapezium A trapezium is a 4-sided shape with straight sides and a pair of parallel sides. For example, If you know the radius of a circle, you can calculate its area using the formula:. If you know the diameter of a circle, you can calculate its area using the formula:. If you know the circumference of a circle, you can calculate its area using the formula:. Example a — Calculate the area of a circle which has a radius of 4cm Solution a — From the question, you know that the circle has a radius of 4cm.
Note: Always remember to present your answer using the correct units of measurement and approximated to a suitable degree of accuracy 3-Calculating the lengths of arcs and the areas of sectors In order to calculate the length of an arc or the area of a sector, you must calculate the value of the angle which is made by the arc or sector at the centre of a circle.
Therefore, the length of the arc and the area of the sector to 2dp are,. Once you know this proportion, you can multiply the circumference of the circle and the area of the circle by this proportion in order to calculate the arc length and sector area respectively: Example a — Calculate the length of the arc and the area of the sector.
Example a — Calculate the volume of the following cone:. The base is a triangle so its area. Exam Tips Make sure you memorise the individual formulae for the shapes mentioned in the worked examples. Remember that perimeter means the distance around a shape. Remember that area is the size of the surface of a shape, and that area is measured in square units. Remember that volume is the amount of 3D space which a shape occupies, and that volume is measured in cubic units.
When calculating the perimeters, areas and volumes of various shapes, make sure you write down ALL of your working out. Topic Summary Calculating the perimeter, area and volume of various shapes requires you to recognise and use the properties of numerous different shapes. The brown border is a fence, while green square is the grass. Think of a two dimensional closed geometric shape, such as a triangle or a square.
The continuous line that forms the border closing the shape is called the perimeter. The length of the perimeter of a shape can be calculated by adding up the length of each side of the shape. Notice the white space inside the perimeter of the shape. That space is called the area. The area of different shapes can be found using different formulas. When calculating the area of a shape, the units will always be squared. The area of the rectangle above is 35 units2.
The perimeter is the distance around the outside of a shape. Perimeter is measured in units e. The area is the amount of space the inside of the shape takes up.
Area is measured in square units e. The below figure represents the difference between area and perimeter. Area Vs Perimeter. The area is the region occupied by the two-dimensional object. Perimeter is the length of the boundary enclosed by the geometric figure. The area is the inner space of an object. Perimeter is the length of the outer boundary of an object. The area represents a two-dimensional object so is measured in square units. Perimeter represents a dimensional object so it is measured in linear units.
Example: Space covered by a garden. Example: length of the boundary of the garden. Perimeter and Area Formulas For all Shapes. Now let us study what is the difference between area and perimeter formulas. There are different types of shapes with different dimensions. So their perimeter and area formulas also differ. Here are the different area and perimeter formulas for all shapes. Given below is the perimeter vs area formula chart which will provide you with the perimeter and area formulas for all shapes.
Name of Geometric shapes. Area Formula.
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