1. Algebra 1 Surface area of solid Figures
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2. Warm Up
1) Calculate the volume of the Triangular prism with altitude = 7.6 cm , base = 11 cm and the height is = 15 cm. 627 cm3
2) The given cylinder has radius = 13 cm and the height = 16 cm. A cone of radius = 9 cm and height = 13 cm is cut from the cylinder. What is the volume of the remaining piece? cm3
3) If the volumes of two cubes are in the ratio 64 : 1, then what is the ratio of their edges? 4:1
4) The radius of a cylinder is decreased to 1/5th of the original radius. How many times will its height increase, if its volume remains the same? 25 times
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3. The surface area of a rectangular solid is expressed in square units.
The surface area of a solid figure is the sum of the areas of all faces of the figure.
An area of study closely related to solid geometry is nets of a solid. Imagine making cuts along some edges of a solid and opening it up to form a plane figure. The plane figure is called the net of the solid.
The surface area of a rectangular solid is expressed in square units.
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4. Surface Area of solid figures
In general,
Surface Area of solid figures
= 2 x area of the base +perimeter of the base x height
If,
B = area of the base
P = perimeter of the base
h = height
SA = Surface Area
Then,
SA = 2B +Ph
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5. If s is the length of one of its sides, then
Cubes
A cube is a three-dimensional figure with all edges of the same length. s s
If s is the length of one of its sides, then
SA = 2(s2) + (4s)s = 6s2
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6. Calculate the surface area of the cube with length of sides = 7 cm.
Volume of the cube = 6s2
= 6 x (7)2
= 6 x 49
= 294
Surface Area of the cube = 294 cm2
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7. Triangular prism b a h c d a b h c d SA = 2( 1 ) + (b + c + d)h 2ab
SA = ab + (b + c + d)h
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8. Calculate the surface area of the regular triangular prism.5 8 10
Surface area of the triangular prism = a x b + (b + c + d)h
= 5 x 8 + ( ) x 10 =
= 280
Surface area of the cuboid = 280 cm2
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9. Now you try!
1) The surface area of a cube is 294 ft2. Find the length of each edge. 7ft
2) Calculate the surface area of the given triangular prism. 645 units2 5 8 11 6 7
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10. Rectangular prism h h w w l l SA = 2B + Ph SA = 2(lw) + (2l + 2w)h
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11. Calculate the surface area of the given rectangular prism.8 4 7
Surface area of the rectangular prism
= 2(lw) + (2l + 2w)h
= 2(8 x 4) + (2 x x 4) x 7
= 2 x 32 + (16 + 8) x 7 =
= 232
Surface area of the rectangular prism = 268 cm2
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12. Regular square prism h h s s SA = 2B + Ph SA = 2(s2) + (4s)h
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13. Calculate the surface area of the given Regular square prism.8 11
Surface area of the Regular square prism
= 2(s2) + (4s)h
= 2(8 x 8) + (4 x 8) x 11
= 2 x x 11 =
= 480
Surface area of the regular square prism = 480 cm2
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14. Regular pentagonal prismh a s a h
SA = 2(1ans) + nsh 2
SA = 2(1a)(5)s + 5sh 2
SA = 5as + 5sh
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15. Calculate the surface area of the given Regular pentagonal prism.8 9 6
Surface area of the Regular square prism
= 5as + 5sh
= 2 x 6 x x 8 x 9
= 2 x x 72 =
= 456
Surface area of the regular square prism = 456 cm2
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16. Now you try!
1) The surface area of a regular square prism is 294 ft2 and height 10 ft. Find the length of each edge of the base. 5.7ft
2) Calculate the surface area of the given Regular pentagonal prism. 180 sq units 4 6 3
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17. Regular triangular pyramids l a s
SA = B + n(1sl) 2
SA = 1as + (3)(1sl)
SA = 1as + 3sl
l = slant height
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18. Calculate the surface area of the given Regular triangular pyramid.5 4 6
Surface area of the Regular triangular pyramid
= 1as + 3sl
= 1 x 4 x x 6 x 5 =
= 63
Surface area of the regular triangular pyramid = 63 cm2
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19. Regular square pyramidh l
SA = B + n(1sl) 2
SA = s2 + (4)(1sl) 2
SA = s2 + 2sl
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20. Calculate the surface area of the given Regular square pyramid.8 h 7
Surface area of the Regular square pyramid
= s2 + 2sl
=8 x x 8 x 7 =
= 176
Surface area of the regular square pyramid = 176 cm2
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21. Now you try!
1) Calculate the surface area of the given Regular triangular pyramid sq units 5 8 9
2) Calculate the surface area of the given Regular square pyramid. 280 sq units 10 h 9
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22. Cylinder h r P r h
SA = 2B + Ph
SA = 2(Π r2) + (2 Π r)h
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23. Calculate the surface area of the given cylinder.5 8
Surface area of the cylinder
= 2(Π r2) + (2 Π r)h
=2 x (3.14 x 5 x 5 ) + (2 x 3.14 x 5 ) x 8 =
= 408.2
Surface area of the cylinder = cm2
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24. Sphere r
SA = 4 Π r2
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25. Calculate the surface area of the given sphere.10
Surface area of the sphere
= 4 Π r2
=4 x 3.14 x 10 x 10
= 1256
Surface area of the sphere = 1256 cm2
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26. 1) Calculate the surface area of the given cylinder. 748 sq units
Now you try!
1) Calculate the surface area of the given cylinder. 748 sq units 7 10
2) Calculate the surface area of the given sphere sq units 8
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27. Assessment
1) What is the perimeter of the floor, if the area of the four walls is equal to 2700 ft2 and its height is 12 ft? 225 ft
2) The perimeter of one face of a cube is 48 cm. What is its surface area? 864 sq cm
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28. 3) The base radius of a cylinder is 2 cm and its height is 5 cm
3) The base radius of a cylinder is 2 cm and its height is 5 cm. What is the resultant surface area of the cylinder, if the radius is increased by 2 times? sq cm
4) Calculate the surface area of the given Regular triangular pyramid sq units 8 7 9
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29. 5) Calculate the surface area of the given Regular pentagonal prism
5) Calculate the surface area of the given Regular pentagonal prism. 225 sq units
4.5 7 3
6) Calculate the surface area of the given Regular square pyramid. 133 sq units 7 h 6
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30. 7) Calculate the surface area of the sphere with radius = 34 cm. 14519
7) Calculate the surface area of the sphere with radius = 34 cm sq cm
8) The base area of a square pyramid is 49 in2. What is the surface area of the pyramid , if the slant height of the pyramid is 12 in? 217 sq in
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31. 9) A rectangular tin sheet of 44 in. long and 20 in
9) A rectangular tin sheet of 44 in. long and 20 in. broad is rolled along its length to form a cylinder by making the opposite edges just touch each other. What is the base radius of the cylinder formed? 5.49 in
10) What is the lateral area of a cube, if the area of each face of the cube is 16 ft2? 64 sq ft
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32. 10 7 3 5
11) The figure shows a rectangular prism with a cylinder which has been removed from it. What is the total surface area of the given solid? Round the answer to the nearest ten. 530 sq units
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33. Let’s review In general, Surface Area of solid figures
= 2 x area of the base +perimeter of the base x height
If,
B = area of the base
P = perimeter of the base
h = height
SA = Surface Area
Then,
SA = 2B +Ph
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34. If s is the length of one of its sides, then
review
Cubes
A cube is a three-dimensional figure with all edges of the same length. s s
If s is the length of one of its sides, then
SA = 2(s2) + (4s)s = 6s2
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35. review Triangular prismb a h c d a b h c d
SA = 2( 1 ) + (b + c + d)h
2ab
SA = ab + (b + c + d)h
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36. review Rectangular prismh l w h
SA = 2B + Ph
SA = 2(lw) + (2l + 2w)h
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37. Regular pentagonal prism
review
Regular pentagonal prism s h a s a h
SA = 2(1ans) + nsh 2
SA = 2(1a)(5)s + 5sh 2
SA = 5as + 5sh
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38. Regular triangular pyramid
review
Regular triangular pyramid l a s l a s
SA = B + n(1sl) 2
SA = 1as + (3)(1sl)
SA = 1as + 3sl
l = slant height
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39. Regular square pyramid
review
Regular square pyramid l s s h l
SA = B + n(1sl) 2
SA = s2 + (4)(1sl) 2
SA = s2 + 2sl
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40. review Cylinder r P h h r SA = 2B + Ph SA = 2(Π r2) + (2 Π r)h
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41. review
Sphere r
SA = 4 Π r2
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42. You did a great job today!
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