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Surface Area

Surface Area. 3D shapes. Instructions for use. There are 9 worked examples shown in this PowerPoint A red dot will appear top right of screen to proceed to the next slide. Click the navigation bar to the left of screen to access relevant slides.

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Surface Area

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  1. Surface Area 3D shapes

  2. Instructions for use • There are 9 worked examples shown in this PowerPoint • A red dot will appear top right of screen to proceed to the next slide. • Click the navigation bar to the left of screen to access relevant slides.

  3. 3 easy steps to calculate the Surface Area of a solid figure • Determine the number of surfaces and the shape of the surfaces of the solid • Apply the relevant formula for the area of each surface • Sum the areas of each surface

  4. 4 rectangular faces and 2 square faces Surface Area – Basic concept rectangle rectangle rectangle square square rectangle Determine the number and shape of the surfaces that make up the solid. When you’ve done all that find the area of each face and then find the total of the areas. It might be easier to think of the net of the solid.

  5. Square prism Find the surface area of this figure with square base 5 cm and  height 18 cm Two square faces Four rectangular faces 18 cm 5 cm

  6. Now sum these areas Rectangular prism Find the surface area of this figure with length 10 cm, width 15 cm and height 12 cm. 20 cm 15 cm 5 cm

  7. Use Pythagoras’ theorem to find the  height of the triangle! 10 cm 8 10 cm 20 cm 6 12 cm 12 cm Hence, total surface area 1 2 3 Determine the number of faces and the shape of each face Sum the areas to give the total surface area Apply the area formulae for each face Recall Triangular Prism Find the surface area of this figure with dimensions as marked.

  8. Use Pythagoras’ theorem to find the  height of the triangular face. P Hence, total surface area 13 13 12 • Each triangular face will have base 10 cm and  height 13 cm. T 5 10 R T 10 R Square Pyramid Find the surface area of this figure with square base 10 cm and  height 12 cm. 4 triangular faces with the same dimensions and 1 square face We need to find the  height of each triangular face. 12

  9. P 8 cm V R 12 cm Q T S 10 cm 8 89 Hence, total surface area 5 10 12 10 8 6 Rectangular Pyramid Find the surface area of this figure with dimensions as marked. • 5 faces altogether: • 2 pairs of congruent triangular faces • 1 rectangular face First find the unknown heights using Pythagoras’ theorem

  10. Required formula: 25 cm Curved surface Curved surface 20 h Hence, total surface area Cylinder Find the surface area of this cylinder with height 25 cm and diameter 20 cm. Think of the net of the cylinder to understand the formula.

  11. l refers to the slant height Required formula Consider the net of the cone l Now calculate the areas. Now sum these areas Use Pythagoras’ theorem l 15 Total surface area: 5 Cone Find the surface area of this cone of height 15 cm radius 5 cm.

  12. Sphere Find the surface area of this sphere with diameter 5 cm. Required formula Easy! The sphere is one continuous surface so just substitute into the formula

  13. Total surface area: Hemisphere Find the surface area of this hemisphere with diameter 5 cm. A hemisphere is a half sphere. But we need to add in the area of the circular base. Required formula

  14. Last slide Use the navigation buttons to repeat selected slides.

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