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Surface area and volume

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Swaraj Routray
Swaraj Routray

This document provides information about calculating the surface area and volume of various 3D shapes including prisms, cylinders, pyramids, and cones. It defines surface area as the total area of the object's surface that would be needed to wrap the entire shape. Various formulas are given to calculate the surface area and volume of different shapes by breaking them down into their 2D components and using the appropriate equations.

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MADE BY X-A STUDENTS 1)SWARAJ ROUTRAY
Surface Area = The total area of the surface of a three- dimensional object (Or think of it as the amount of paper youll need to wrap the shape.) Prism = A solid object that has two identical ends and all flat sides. We will start with 2 prisms a rectangular prism and a triangular prism.
Rectangular Prism Triangular Prism
Like dice, there are six sides (or 3 pairs of sides)
Surface area and volume
SA = 2lw + 2lh + 2wh 10 - length 5 - width 6 - height SA = 2lw + 2lh + 2wh SA = 2 (10 x 5) + 2 (10 x 6) + 2 (5 x 6) = 2 (50) + 2(60) + 2(30) = 100 + 120 + 60 = 280 units squared
10 ft 12 ft 22 ft SA = 2lw + 2lh + 2wh = 2(22 x 10) + 2(22 x 12) + 2(10 x 12) = 2(220) + 2(264) + 2(120) = 440 + 528 + 240 = 1208 ft squared
2 bases (triangular) 3 sides (rectangular)
Surface area and volume
15ft Area Triangles = 遜 (b x h) = 遜 (12 x 15) = 遜 (180) = 90 Area Rect. 1 = b x h = 12 x 25 = 300 Area Rect. 2 = 25 x 20 = 500 SA = 90 + 90 + 300 + 500 + 500 SA = 1480 ft squared
Surface area and volume
Surface area is like the amount of paper youll need to wrap the shape. You have to take apart the shape and figure the area of the parts. Then add them together for the Surface Area (SA)
A cylinder has 2 main parts. A rectangle and A circle well, 2 circles really. Put together they make a cylinder.
Think of the Cylinder as a soup can. You have the top and bottom lid (circles) and you have the label (a rectangle wrapped around the can). The lids and the label are related. The circumference of the lid is the same as the length of the label .
Formula for Area of Circle A= r2 = 3.14 x 32 = 3.14 x 9 = 28.26 But there are 2 of them so 28.26 x 2 = 56.52 units squared
This has 2 steps. To find the area we need base and height. Height is given (6) but the base is not as easy . Notice that the base is the same as the distance around the circle (or the Circumference).
Formula is C = x d = 3.14 x 6 (radius doubled) = 18.84 Now use that as your base. A = b x h = 18.84 x 6 (the height given) = 113.04 units squared
SA = ( d x h) + 2 ( r2 ) Label Lids (2) Area of Rectangle Area of Circles
SA = ( d x h) + 2 ( r2 ) = (3.14 x 22 x 14) + 2 (3.14 x 112 ) = (367.12) + 2 (3.14 x 121) = (367.12) + 2 (379.94) = (367.12) + (759.88) = 1127 cm2
Surface area and volume
A pyramid has 2 shapes: One (1) square & Four (4) triangles
Since you know how to find the areas of those shapes and add them. Or . . . .
you can use a formula SA = 遜 lp + B Where l is the Slant Height and p is the perimeter and B is the area of the Base
Perimeter = (2 x 7) + (2 x 6) = 26 Slant height l = 8 SA = 遜 lp + B = 遜 (8 x 26) + (7 x 6) *area of the base* = 遜 (208) + (42) = 104 + 42 = 146 units 2 6 7 8 5
6 6 18 10 SA = 遜 lp + B = 遜 (18 x 24) + (6 x 6) = 遜 (432) + (36) = 216 + 36 = 252 units2
The number of cubic units needed to fill the shape. Find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. There are 24 cubes in the prism, so the volume is 24 cubic units. 2 x 3 x 4 = 24 2 height 3 width 4 length
VOLUME OF A PRISMVOLUME OF A PRISM The volumeThe volume VV of a prism is theof a prism is the area of its basearea of its base BB times its heighttimes its height hh.. VV == BhBh Note the capital letter stands for the AREA of theNote the capital letter stands for the AREA of the BASE not the linear measurement.BASE not the linear measurement.
4 ft - width 3 ft - height 8 ft - length V = Bh Find area of the base = (8 x 4) x 3 = (32) x 3 Multiply it by the height = 96 ft3
12 cm 10 cm 22 cm V = Bh = (22 x 10) x 12 = (220) x 12 = 2640 cm3
VOLUME OF A CYLINDERVOLUME OF A CYLINDER The volumeThe volume VV of a cylinder is the areaof a cylinder is the area of its base,of its base, rr22 , times its height, times its height hh.. VV == rr22 hh Notice thatNotice that rr22 is the formula for areais the formula for area of a circle.of a circle.
7 cm - height 13 cm - radius V = r2 h Start with the formula V = 3.14 x 132 x 7 substitute what you know = 3.14 x 169 x 7 Solve using order of Ops. = 3714.62 cm3
Remember that Volume of a Prism is B x h where b is the area of the base. You can see that Volume of a pyramid will be less than that of a prism. How much less? Any guesses?
Volume of a Pyramid:- V = (1/3) Area of the Base x height V = (1/3) Bh Volume of a Pyramid = 1/3 x Volume of a Prism If you said 2/3 less, you win! + + =
Find the volume of the square pyramid with base edge length 9 cm and height 14 cm. The base is a square with a side length of 9 cm, and the height is 14 cm. V = 1/3 Bh = 1/3 (9 x 9)(14) = 1/3 (81)(14) = 1/3 (1134) = 378 cm3 14 cm
In mathematIcs the art of understandIng problems Is easIer than that of solvIng them. so sImply solve them ! ! ! !

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Surface area and volume

  • 1. MADE BY X-A STUDENTS 1)SWARAJ ROUTRAY
  • 2. Surface Area = The total area of the surface of a three- dimensional object (Or think of it as the amount of paper youll need to wrap the shape.) Prism = A solid object that has two identical ends and all flat sides. We will start with 2 prisms a rectangular prism and a triangular prism.
  • 4. Like dice, there are six sides (or 3 pairs of sides)
  • 6. SA = 2lw + 2lh + 2wh 10 - length 5 - width 6 - height SA = 2lw + 2lh + 2wh SA = 2 (10 x 5) + 2 (10 x 6) + 2 (5 x 6) = 2 (50) + 2(60) + 2(30) = 100 + 120 + 60 = 280 units squared
  • 7. 10 ft 12 ft 22 ft SA = 2lw + 2lh + 2wh = 2(22 x 10) + 2(22 x 12) + 2(10 x 12) = 2(220) + 2(264) + 2(120) = 440 + 528 + 240 = 1208 ft squared
  • 10. 15ft Area Triangles = 遜 (b x h) = 遜 (12 x 15) = 遜 (180) = 90 Area Rect. 1 = b x h = 12 x 25 = 300 Area Rect. 2 = 25 x 20 = 500 SA = 90 + 90 + 300 + 500 + 500 SA = 1480 ft squared
  • 12. Surface area is like the amount of paper youll need to wrap the shape. You have to take apart the shape and figure the area of the parts. Then add them together for the Surface Area (SA)
  • 13. A cylinder has 2 main parts. A rectangle and A circle well, 2 circles really. Put together they make a cylinder.
  • 14. Think of the Cylinder as a soup can. You have the top and bottom lid (circles) and you have the label (a rectangle wrapped around the can). The lids and the label are related. The circumference of the lid is the same as the length of the label .
  • 15. Formula for Area of Circle A= r2 = 3.14 x 32 = 3.14 x 9 = 28.26 But there are 2 of them so 28.26 x 2 = 56.52 units squared
  • 16. This has 2 steps. To find the area we need base and height. Height is given (6) but the base is not as easy . Notice that the base is the same as the distance around the circle (or the Circumference).
  • 17. Formula is C = x d = 3.14 x 6 (radius doubled) = 18.84 Now use that as your base. A = b x h = 18.84 x 6 (the height given) = 113.04 units squared
  • 18. SA = ( d x h) + 2 ( r2 ) Label Lids (2) Area of Rectangle Area of Circles
  • 19. SA = ( d x h) + 2 ( r2 ) = (3.14 x 22 x 14) + 2 (3.14 x 112 ) = (367.12) + 2 (3.14 x 121) = (367.12) + 2 (379.94) = (367.12) + (759.88) = 1127 cm2
  • 21. A pyramid has 2 shapes: One (1) square & Four (4) triangles
  • 22. Since you know how to find the areas of those shapes and add them. Or . . . .
  • 23. you can use a formula SA = 遜 lp + B Where l is the Slant Height and p is the perimeter and B is the area of the Base
  • 24. Perimeter = (2 x 7) + (2 x 6) = 26 Slant height l = 8 SA = 遜 lp + B = 遜 (8 x 26) + (7 x 6) *area of the base* = 遜 (208) + (42) = 104 + 42 = 146 units 2 6 7 8 5
  • 25. 6 6 18 10 SA = 遜 lp + B = 遜 (18 x 24) + (6 x 6) = 遜 (432) + (36) = 216 + 36 = 252 units2
  • 26. The number of cubic units needed to fill the shape. Find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. There are 24 cubes in the prism, so the volume is 24 cubic units. 2 x 3 x 4 = 24 2 height 3 width 4 length
  • 27. VOLUME OF A PRISMVOLUME OF A PRISM The volumeThe volume VV of a prism is theof a prism is the area of its basearea of its base BB times its heighttimes its height hh.. VV == BhBh Note the capital letter stands for the AREA of theNote the capital letter stands for the AREA of the BASE not the linear measurement.BASE not the linear measurement.
  • 28. 4 ft - width 3 ft - height 8 ft - length V = Bh Find area of the base = (8 x 4) x 3 = (32) x 3 Multiply it by the height = 96 ft3
  • 29. 12 cm 10 cm 22 cm V = Bh = (22 x 10) x 12 = (220) x 12 = 2640 cm3
  • 30. VOLUME OF A CYLINDERVOLUME OF A CYLINDER The volumeThe volume VV of a cylinder is the areaof a cylinder is the area of its base,of its base, rr22 , times its height, times its height hh.. VV == rr22 hh Notice thatNotice that rr22 is the formula for areais the formula for area of a circle.of a circle.
  • 31. 7 cm - height 13 cm - radius V = r2 h Start with the formula V = 3.14 x 132 x 7 substitute what you know = 3.14 x 169 x 7 Solve using order of Ops. = 3714.62 cm3
  • 32. Remember that Volume of a Prism is B x h where b is the area of the base. You can see that Volume of a pyramid will be less than that of a prism. How much less? Any guesses?
  • 33. Volume of a Pyramid:- V = (1/3) Area of the Base x height V = (1/3) Bh Volume of a Pyramid = 1/3 x Volume of a Prism If you said 2/3 less, you win! + + =
  • 34. Find the volume of the square pyramid with base edge length 9 cm and height 14 cm. The base is a square with a side length of 9 cm, and the height is 14 cm. V = 1/3 Bh = 1/3 (9 x 9)(14) = 1/3 (81)(14) = 1/3 (1134) = 378 cm3 14 cm
  • 35. In mathematIcs the art of understandIng problems Is easIer than that of solvIng them. so sImply solve them ! ! ! !