1 / 23

Surface

This guide provides formulas and calculations for finding the surface areas of various solids, including cubes, cuboids, cones, cylinders, spheres, hemispheres, and combinations of these shapes.

mfenton
Download Presentation

Surface

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Surface Areas -- FORMULAE --

  2. Surface Areas Surface Areas Of Some Solids Surface Areas Of Some Combined Solids EXIT

  3. CUBE CUBE Surface Area We will need to find the surface area of the top, base and sides. Area of the top and bottom is 2a2 Area of sides (CSA) is 4a2 Therefore the formula is:6a2 Volume V = a 3 a a a a MAIN MENU NEXT

  4. CUBOID Cuboid Surface Area We will have to calculate the area of sides, top and base. Area of sides = (CSA) is 2(lh+bh) Area of top and base is 2(lb) Therefore the formula is: 2(lb+lh+bh) Volume v = lbh MAIN MENU NEXT

  5. CONE TSA = תr(s+r) NEXT MAIN MENU

  6. CYLINDER CSA = 2πr2 NEXT MAIN MENU

  7. SPHERE NEXT MAIN MENU

  8. HEMISPHERE Surface Area We need to find the outer surface area and the area of the base. Outer surface area (CSA) is 2 π r^2 Area of the base is π r^2 Therefore the formula is 3 π r^2 Volume V = πr^3 MAIN MENU

  9. SURFACE AREA OF A COMBINATION OF SOLIDS SURFACE AREA OF -- MAIN MENU NEXT

  10. SURFACE AREA OF A COMBINATION OF SOLIDS SURFACE AREA OF -- MAIN MENU BACK

  11. A Cylinder Surmounted By A Cone l h Surface Area of the model = CSA of cone + CSA of cylinder = πrl + 2πrh = π r ( l + 2h ) r NOTE: The cylinder is hollow BACK

  12. A Solid Cylinder With A Conical Cavity Surface Area of the model = CSA of the cylinder + CSA Of the cone + Area of the cylinder’s base = 2πrh + πrl + πr2 = πr ( 2h + l + r ) h l r BACK

  13. A Sphere Attatched To A Cone Surface Area of the model = CSA of hemisphere + CSA of the cone = 2πr2 + πrl = πr ( 2r + l ) l r BACK

  14. A Round Bottom Flask r Surface area of the model = CSA of the cylinder + Surface area of the sphere – Area of the cylinder’s base = 2 πrh + 4 πr2 – πr2 = πr ( 2h – r ) + 4πr2 h R BACK

  15. A Cylinder Surmounted By Another Cylinder r h Surface area of the model = TSA of the the larger cylinder + TSA of the smaller cylinder – Area of the smaller cylinder’s base = 2πRH + 2πR2 + 2πrh + 2πr2 – πr2 = 2πR ( H + R ) + 2πr ( h + r ) H R BACK

  16. A Cylinder With Cones On Its Ends Surface area of the model = CSA of the cylinder + CSA of both the cones = 2πrh + 2πrl = 2πr ( h + l ) h l r NOTE- The cones are of the same dimensions BACK

  17. A Cylinder With Hemispherical Cavities Surface area of the model = CSA of the cylinder + CSA of the two hemispheres = 2πrh + 2 ( 2πr2 ) = 2πrh + 4πr2 = 2πr ( h + 2r ) h BACK r

  18. Two Cubes Of Similar Dimensions When two cubes are joined, they form a cuboid. In the given model when the two cubes of side ‘a’ are joined, we get a cuboid of dimension > l = a + a b = a h = a a a So the model’s surface area is 2 ( lb + bh +hl ) = 2 { ( a + a ) a + a2 + a ( a + a) } = 2 ( 2a2 + a2 + 2a2 ) = 2 ( 5a2) = 10a2 a BACK

  19. A Capsule Surface area of the model = CSA of the cylinder + CSA of the two hemispheres of the same dimension = 2πrh + 2πr2 + 2πr2 = 2πrh + 4πr2 = 2πr ( h + 2r ) r r h BACK

  20. Hemispherical Depression In A Cuboid Surface area of the model = TSA of the cuboid + CSA of the hemisphere - CSA of the top of the hemisphere = 2 ( lb + hl + hb ) + 2πr2 – πr2 = 2 ( lb + hl + hb ) + πr2 r h b l BACK

  21. A Cuboid Surmounted By A Hemisphere Surface area of the model = TSA of the cuboid + CSA of the hemisphere - CSA of the top of the hemisphere = 2 ( lb + hl + hb ) + 2πr2 – πr2 = 2 ( lb + hl + hb ) + πr2 r h b l BACK

  22. A Hollow Cylinder Surmounted By A Hemisphere r Surface area of the model = CSA of the cylinder + CSA of the hemisphere = 2πrh + 2πr2 = 2πr ( h + r ) h r BACK

  23. Thank you - Dhruv Sahdev

More Related