Algebra 1 Surface area of solid Figures

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Algebra 1Surface area of solid Figures
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Warm Up
1) Calculate the volume of the Triangular prism
with altitude 7.6 cm , base 11 cm and the
height is 15 cm.
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?
3) If the volumes of two cubes are in the ratio
64 1, then what is the ratio of their edges?
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?
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Surface area
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 express
ed in square units.
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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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Cubes
A cube is a three-dimensional figure with all
edges of the same length.
If s is the length of one of its sides, then SA
2(s2) (4s)s 6s2
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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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Triangular prism
SA 2( 1 ) (b c d)h 2ab
SA ab (b c d)h
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Calculate the surface area of the regular
triangular prism.
Surface area of the triangular prism a x b (b
c d)h 5 x 8
(8 8 8) x 10 40 240 280
Surface area of the cuboid 280 cm2
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Now you try!
1) The surface area of a cube is 294 ft2. Find
the length of each edge.
2) Calculate the surface area of the given
triangular prism.
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Rectangular prism
SA 2B Ph
SA 2(lw) (2l 2w)h
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Calculate the surface area of the given
rectangular prism.
Surface area of the rectangular prism 2(lw)
(2l 2w)h 2(8 x
4) (2 x 8 2 x 4) x 7 2 x 32 (16 8) x 7
64 168 232
Surface area of the rectangular prism 268 cm2
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Regular square prism
SA 2B Ph
SA 2(s2) (4s)h
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Calculate the surface area of the given Regular
square prism.
Surface area of the Regular square prism 2(s2)
(4s)h 2(8 x 8)
(4 x 8) x 11 2 x 64 32 x 11 128 352
480
Surface area of the regular square prism 480 cm2
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Regular pentagonal prism
SA 2(1ans) nsh 2
SA 2(1a)(5)s 5sh 2
SA 5as 5sh
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Calculate the surface area of the given Regular
pentagonal prism.
Surface area of the Regular square prism 5as
5sh 2 x 6 x 8 5 x 8
x 9 2 x 48 5 x 72 96 360 456
Surface area of the regular square prism 456 cm2
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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.
2) Calculate the surface area of the given
Regular pentagonal prism.
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Regular triangular pyramid
SA B n(1sl) 2
SA 1as (3)(1sl) 2 2
SA 1as 3sl 2 2
l slant height
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Calculate the surface area of the given Regular
triangular pyramid.
Surface area of the Regular triangular pyramid
1as 3sl 2 2 1 x 4 x 6 3 x 6 x 5
2 2 18 45 63
Surface area of the regular triangular pyramid
63 cm2
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Regular square pyramid
SA B n(1sl) 2
SA s2 (4)(1sl) 2
SA s2 2sl
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Calculate the surface area of the given Regular
square pyramid.
Surface area of the Regular square pyramid s2
2sl 8 x 8 2 x 8 x 7 64 112 176
Surface area of the regular square pyramid 176
cm2
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Now you try!
1) Calculate the surface area of the given
Regular triangular pyramid.
2) Calculate the surface area of the given
Regular square pyramid.
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Cylinder
SA 2B Ph
SA 2(? r2) (2 ? r)h
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Calculate the surface area of the given cylinder.
Surface area of the cylinder 2(? r2) (2 ? r)h
2 x (3.14 x 5 x 5 ) (2 x 3.14 x 5 ) x 8
157 251.2 408.2
Surface area of the cylinder 408.2 cm2
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Sphere
SA 4 ? r2
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Calculate the surface area of the given sphere.
Surface area of the sphere 4 ? r2 4 x 3.14 x
10 x 10 1256
Surface area of the sphere 1256 cm2
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Now you try!
1) Calculate the surface area of the given
cylinder.
2) Calculate the surface area of the given sphere.
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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?
2) The perimeter of one face of a cube is 48 cm.
What is its surface area?
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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?
4) Calculate the surface area of the given
Regular triangular pyramid.
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5) Calculate the surface area of the given
Regular pentagonal prism.
6) Calculate the surface area of the given
Regular square pyramid.
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6) Calculate the surface area of the sphere with
radius 34 cm.
7) 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?
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8) 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?
9) What is the lateral area of a cube, if the
area of each face of the cube is 16 ft2?
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10) 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.
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Lets 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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review
Cubes
A cube is a three-dimensional figure with all
edges of the same length.
If s is the length of one of its sides, then SA
2(s2) (4s)s 6s2
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review
Triangular prism
SA 2( 1 ) (b c d)h 2ab
SA ab (b c d)h
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review
Rectangular prism
SA 2B Ph
SA 2(lw) (2l 2w)h
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review
Regular pentagonal prism
SA 2(1ans) nsh 2
SA 2(1a)(5)s 5sh 2
SA 5as 5sh
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review
Regular triangular pyramid
SA B n(1sl) 2
SA 1as (3)(1sl) 2 2
SA 1as 3sl 2 2
l slant height
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review
Regular square pyramid
SA B n(1sl) 2
SA s2 (4)(1sl) 2
SA s2 2sl
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review
Cylinder
SA 2B Ph
SA 2(? r2) (2 ? r)h
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review
Sphere
SA 4 ? r2
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You did a great job today!