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Wednesday 19 April 2023
of a Prism and of a Prism and CylinderCylinder
Surface Surface areaarea
The prism has 3 rectangular and 2 triangular faces.
This is one way of drawing the net.
This is a triangular prism.To find the surface area we need to be able to visualise the faces.
This is one way of drawing the net.
This is a triangular prism.To find the surface area we need to be able to visualise the faces.
The surface area is the sum of the areas of 3 rectangles and 2 triangles.
The cylinder has 2 flat surfaces and 1 curved surface.
top
How many surfaces does a solid cylinder have?
base
The curved surface unwraps to a rectangle.
curved surfaceUnwrap the
cylinder . . . to get this
e.g.
Tip: No square, it’s a length !
To find the surface area of a cylinder we need some circle facts.
Reminders:
rArea = r2
Tip: Area, so a square!
Circumference = d
When we are calculating the values, unless we are asked for an estimate, we
use the button on the calculator.
We must work to at least one more decimal place or significant figure than we need in the
final answer.
( Reminder: d = 2r )
top
base
3cm
8cm
r = 3
curved surface
8cm
r = 3
Area of the base = r2 = 28·27 cm2
Length of rectangle = d
= (6)= 18·85
cm2
Total area = 150·80 + 28·27 + 28·27 = 207·3 cm2 ( 1 d.p.)
Tip: Leave this answer on your calculator so you don’t have to type it in again at the next stage.
e.g. Find the surface area, giving the answer correct to 1 decimal place.
= (3)2= 150·80 cm2
d
Area of rectangle = 18·85 8
SUMMARY
The surface area of a solid cylinder is made up of:• 2 circles
• 1 curved surface that unwraps to a rectangle.
The area of each circle is r2.
The length of the rectangle is d.
The surface area of a triangular prism is made up of:• 3
rectangles• 2 triangles
EXERCISE
1.(a) Draw and label, with names and lengths, the triangle and 3 rectangles that make the different faces of the prism shown below. ( The drawings need not be to scale. )(b) How many faces has the prism?(c) Find the surface area of the prism.
1m
30cm
40cm
Solution:
EXERCISE
30cm
40cm
By Pythagorasc2 = 302 + 402
= 2500
= 50 cmc = √ 2500 cm
c50 cm
1m
30cm
40 cm
end face
1m
30cm
40 cm
Solution:
Area of 1 end = ½ 30 40 = 600 cm2Area of sloping face = 100 50 = 5000
cm2Area of base = 100 30 = 3000
cm2
Surface area = 600 + 600 + 5000 + 3000 + 4000 = 13200 cm2
EXERCISE
1m
50cm
40cm
30cm
Area of vertical face = 100 40 = 4000
cm2
The prism has 5 faces
30cm
40cm
end face
sloping face
vertical face
base
50 cm
EXERCISE
2(i) Draw and label the 3 surfaces of the cylinders shown in the diagram. ( They need not be to scale. )
(ii) Find the surface area of each cylinder giving your answers correct to 1 decimal place.
50cm
10cm
9m
3m
(a)
(b)
EXERCISE
50cm
10cm
Solutions: (a
)
Area of base or top = r2 = (10)2 = 314·16Length of rectangle = d = (20 = 62·83Area of rectangle = 62·83 50 = 3141·59
Total area =
r = 10cm
base and top
curved surface
d
50cm
r = 10cm
EXERCISE
50cm
10cm
Solutions: (a
)
Area of base or top = r2 = (10)2 = 314·16Length of rectangle = d = (20 = 62·83Area of rectangle = 62·83 50 = 3141·59
2 314·16 + 3141·59 = 3769·9 cm2 ( 1 d.p.)
Total area =
r = 10cm
base and top
curved surface
d
50cm
r = 10cm
EXERCISE
9m
3m
Solutions:(b
)base and top
curved surface
d
9mr = 3m
Area of base or top = r2 = (3)2 = 28·27Length of rectangle = d = (6 = 18·85Area of rectangle = 18·85 9 = 169·65
Total area =
r = 3m
EXERCISE
9m
3m
Solutions:(b
)
curved surface
d
9m
Area of base or top = r2 = (3)2 = 28·27Length of rectangle = d = (6 = 18·85Area of rectangle = 18·85 9 = 169·65
2 28·27 + 169·65 = 226·2 m2 ( 1 d.p.)
Total area =
base and top
r = 3m
r = 3m
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