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SURFACE AREA AND VOLUME 2

SURFACE AREA AND VOLUME 2. Volume of a pyramid. h. Calculate the volume of the rectangular-based pyramid. E. 6 cm. D. C. 4 cm. A. 5 cm. B. Surface area of a pyramid. h. Surface area = sum of the areas of all the faces of the pyramid.

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SURFACE AREA AND VOLUME 2

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  1. SURFACE AREA AND VOLUME 2

  2. Volume of a pyramid h

  3. Calculate the volume of the rectangular-based pyramid. E 6 cm D C 4 cm A 5 cm B

  4. Surface area of a pyramid h Surface area = sum of the areas of all the faces of the pyramid

  5. Calculate the surface area of the rectangular-based pyramid. E First find the length of EX and EY. Use Pythagoras on triangle EOX. 6 cm D C Use Pythagoras on triangle EOY. O X 4 cm A B Y 5 cm

  6. E Area of rectangle ABCD = 4 × 5 NET OFPYRAMID = 20 cm2 Area of triangle BCE = ½ × 4 × 6.5 = 13 cm2 6.325 D C Area of triangle CDE = ½ × 5 × 6.325 5 cm = 15.81 cm2 6.5 6.5 4 cm E E A B Surface area = sum of areas of faces = 20 + 13 + 13 + 15.81 + 15.81 6.325 = 77.6 cm2 E

  7. Volume of a cone h r

  8. Calculate the volume of the cone. 7 cm 4 cm

  9. Surface area of a cone The surface of a cone is made from a flat circular base and a curved surface. The curved surface is made from a sector of a circle. CURVED SURFACE = + FLAT BASE Curved surface area of a cone = , where is the slant height Total surface area of a cone =

  10. Calculate a the curved surface area of the cone, b the total surface area of the cone. a First calculate the slant height using Pythagoras. 12 cm Curved surface area 5 cm b Total surface area

  11. The straight edges of the sector are joined together to make a cone. Calculate a the curved surface area of the cone, b the radius of the base of the cone, c the height of the cone. 280o 4 cm a Curved surface area = area of sector 4 cm c Using Pythagoras b Curved surface area 4 3.11

  12. When you make a cut parallel to the base of a cone and remove the top part, the part that is left is called a frustum. FRUSTUM Volume of frustum = volume of large cone – volume of smaller cone

  13. 3 Calculate the volume of the frustum. All lengths are in cm. 8 6 You must first find the height of the smaller cone using similar triangles. 3 Volume of large cone 8 6 Volume of small cone Volume of frustum

  14. Volume and surface area of a sphere Volume of a sphere Volume of a hemisphere Curved surface area of a hemisphere Surface area of a sphere Volume and surface area of a hemisphere A hemisphere is half a sphere.

  15. The sphere has radius 10 cm. Calculate a the volume of the sphere, b the surface area of the sphere. a Volume b Surface area

  16. The solid hemisphere has radius 6 cm. Calculate a the volume of the hemisphere, b the curved surface area of the hemisphere, c the total surface area of the hemisphere. 6 cm a Volume b Curvedsurface area c Totalsurface area = area of base circle + curved surface area

  17. The solid is made from a cylinder and a hemisphere. The cylinder has a height of 8 cm and a radius of 3 cm. Calculate the volume of the solid. Volume of cylinder Volume of hemisphere Total volume

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