surface area and volume (interactivo) - junta de andalucía · surface area and volume....
TRANSCRIPT
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SURFACE AREA AND VOLUME
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Instructions
1. Listen to teacher’s directions before continuing, raise your hand and ask questions every time you need.
2. Get your worksheet ready to record the information.
3. Go to the next page only if you have finished the one you are working on.
4. Do not rush, you have enough time to finish.
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3-D Objects
PRISM
PYRAMID
CYLINDER
CONE
SPHERE
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THREE-DIMENSIONAL OBJECTS
A three-dimensional object is a figure that has depth in addition to width and height.
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The surface area of a 3-D object is the total area of all the faces of the figure.
SURFACE AREA
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The volume is a measure of how much space a 3-D object takes up.
VOLUME
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PRISM
A prism is a solid with two congruent parallel bases that are polygons.
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PRISM
base
height
h
P = perimeter
B = area Surface Area SA = 2B + Ph
Volume V = B h
LATERAL AREA
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PRISM
EXAMPLE
Find the surface area and volume of a slab of stone
measuring 3 m in length, 2 m in breadth and 25 cm in
thickness.
Solution:
l = 3 m
w = 2 m
h = 25 cm = 0.25 m
Surface area
SA= 2B + Ph = 2 (3 · 2) + (3+3+2+2)· 0.25 = 14.5 sq m.
Volume
V= l· w· h = 3· 2· 0.25 = 1.5 cu m.
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PYRAMID
A pyramid is a solid having a polygonal base and triangle-shaped sides.
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PYRAMID
lateral
height
l
base
P = perimeter
B = area
Surface Area SA = B + 1/2 Pl
Volume V = 1/3 B h
LATERAL AREA
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PYRAMID
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CYLINDER
A cylinder is a solid with two circular bases that are parallel.
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CYLINDER
height
h
radius
r
Surface Area SA = 2πr2+2πrh
Volume V = π r2 h
LATERAL AREA
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CYLINDER
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CONE
A cone is solid having a circular base and a single vertex.
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CONE
radius
r
lateral
height
lSurface Area SA = πr2 + πrl
Volume V = 1/3 πr2 h
LATERAL AREA
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CONE
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SPHERE
A sphere is a solid having all of its points the same distance from its center, this distance is called radius.
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SPHERE
radius
r Surface Area SA = 4 π r2
Volume V = 4 /3 π r3
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SPHERE
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FORMULAS
Surface Area Volume
Prism 2B + Ph B h
Pyramid B + 1/2 Pl 1/3 B h
Cylinder 2πr2 + 2πr h π r2 h
Cone πr2 + πrl 1/3 πr2 h
Sphere 4 π r2 4 /3 π r3
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