We looked at how to find the surface area of prisms.
There is a lesson on Mymaths explaining how to calculate the surface area of prisms by thinking about the shape of their nets. We concentrated on cuboids and triangular prisms. We will look at cylinders in a future lesson.
To find the total surface area of any prism you have to find the area of each individual face of the shape and then add them together.
For example, to work out the surface area of this cuboid with sides of length 3, 4 & 5.
We can think of the cuboid as a net.
Then work out the area of each face (remember that on a cuboid opposite faces are equal)
4 x 5 = 20
4 x 5 = 20
4 x 3 = 12
4 x 3 = 12
3 x 5 = 15
3 x 5 = 15
To find the total surface area just add the areas together
20 + 20 + 12 + 12 + 15 + 15 = 94
The surface area of a triangular prism is done in the same way, but remember that the area of a triangle = ½ base x height
In the lesson today we were calculating the volume of prisms.
A prism is any 3D shape that has a constant cross section (when you slice it the cross section is the same all the way through). Some examples of prisms are: cuboids, triangular prisms and cylinders.
The volume of any prism is found by the following general formula:
Volume = area of cross section x length
For example to find the volume of a triangular prism:
Volume = Area of cross section x length
Volume = ½ b x h x L
Volume = ½ x 7 x 4 x 5
Volume =70
More details and example are available on the Mymaths lesson on volumes of prisms.
Today we looked at how to find the area of a circle.
We started by seeing that if you cut a circle up into lots of segments and place them next to each other you get a shape that looks like a rectangle. The more segments the circle is divided into to closer to a rectangle it becomes.
The width of the rectangle is the same as the radius of the circle and the length of the rectangle is half of the circumference of the circle. The circumference is 2∏r so half the circumference is ∏r.
The formula for the area of the circle is then the same the area of this rectangle, which is ∏r x r
So the area of a circle is found by the formula:
Area of circle = ∏r x r = ∏r²
For example:
To find the area of this circle with radius 4cm
Area = ∏r²
Area = ∏ x 4²
Area = ∏ x 16
Area = 50.3 cm² (1dp)
For more details, example and questons to try visit the Mymaths lesson on area of a circle
Today’s lesson was about the circumference of a circle. We looked at how the circumference is the distance around the outside of the circle and discussed the connection between the diameter and circumference of a circle.
We discussed that Pi (∏), which is the number that connects the diameter and circumference is approximately 3. Sometimes you are required to use an accurate value for Pi on your calculator and sometimes you are asked to use an approximate value such as 3.14.
Calculating the circumference of a circle
To calculate the circumference of a circle we use the formula
Circumference = ∏ x Diameter
C = ∏D
(or C = 2∏r if you have the radius)
So for this circle the circumference is calculated by
C = ∏ x 6
C = 18.8 cm (1dp)
For more help or to see how the circumference and the diameter are connected see the Mymaths lesson.
We looked at the formula for calculating the area of a trapesium and then used that and the formulas we learned last lesson, for areas of triangles and parallelograms, to calculate the areas of some compound shapes.
Area of a trapesium
To find the area of a trapezium we use the formula
Area = ½ (a + b) x height
So for this trapezium
Area = ½ (5 + 7) x8
Area = 48cm²
Mymaths has a lesson on areas of trapeziums.
We revised the methods of calculating the areas of triangles and parallelograms.
We looked at how the areas of each relate to the area of the rectangle that surrounds them and then saw how the formulas are derived from the formula for the area of a rectangle.
Area of a triangle
To find the are of the triangle we use the formula
Area = ½ base x height
So for this traingle
Area = ½ 6 x4
Area = 12cm²
Area of a parallelogram
To find the are of the parallelogram we use the formula
Area = base x height
(make sure you use the perpendicular height)
So for this parellelogram
Area = 12 x 8
Area = 96cm²
You can read more about the area of triangles and parallelograms on Mymaths.co.uk
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Welcome to the class blog for Mr Dolan’s year 11 Maths group.
This blog is a place for us as a class to record the things we look at in lessons, homeworks that are set and other information that will be useful for ensuring that every member of the class achieves their full potential in Maths this year.
Congratulations and well done on the results from Module 3. The class as a whole did very well and has a strong base to get good grades overall.
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