What Is The Total Surface Area Of The Drawing?
What is surface surface area?
- A face is 1 of the apartment or curved surfaces that make up a 3D shape
- The surface surface area of a 3D shape is the sum of the areas of all the faces that make up the shape
- Annotation how nosotros are carrying a second idea (area) into 3 dimensions here
Surface area – cuboids, pyramids, and prisms
- In cuboids, polygonal-based pyramids, and polygonal-based prisms (ie. pyramids and prisms whose bases have straight sides), all the faces are flat
- The surface expanse is found simply by adding upward the areas of these apartment faces
- When calculating surface surface area, it can be very helpful to draw a 2nd net for the 3D shape in question
- For example:
- The base of a square-based pyramid is 15 cm on a side
- The triangular faces are identical isosceles triangles, each with a summit (from the base to the meridian of the pyramid) of 23 cm
- Detect the total surface area of the pyramid
- Draw a net for the shape:
Surface area of square base =15two = 225 cm2
Area of one triangular confront = ½ base × height = ½ × 15 × 23 =172.5 cmtwo
Full surface area =225 + iv × 172.5 = 915 cm2
Surface area – cylinders, cones, and spheres
- All three of these shapes have curved faces, so we have to be a footling more conscientious when computing their surface areas
i. The net of a cylinder consists of two circles and a rectangle:
- The total area of a cylinder with base radius r and acme h is therefore given by:
Total surface area of a cylinder= 2πrii + 2πrh
2. The net of a cone consists of the round base forth with the curved surface surface area:
- The length l in that diagram is known equally the slant elevation (while h is the vertical height of the cone)
- To detect the area of a cone with base radius r and camber height l, nosotros use the formulas:Curved surface expanse of a cone = πrl
Total surface surface area of a cone = πrtwo+πrl
3. To notice the surface expanse of a sphere with radius r, use the formula:
Surface surface area of a sphere=4πr2
Exam Tip
The formula for the surface area of a sphere or the curved area of a cone will be given to y'all in an exam question if you need it. The rest of the formulas here come from what you should already know most areas of rectangles, triangles, and circles.Be conscientious when calculating the surface area of a hemisphere:
The total expanse consists of the curved function (half of a sphere) PLUS the flat circular confront – and then the total surface area is 3πr2
Worked Instance
Source: https://www.savemyexams.co.uk/notes/igcse-maths-edexcel-new/4-geometry/4-15-3d-shapes-surface-area/4-15-1-3d-shapes-surface-area/
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