sa = 2 l w + 2 l h +2 w h
DESCRIPTION
Surface Area of Rectangular Prisms. Example : Jeff bought his mom a box of chocolates for Mother’s Day ( aww ). If the box is rectangular-prism-shaped with a length of 5.4 cm, a width of 2.8 cm, and a height of 1.5 cm, how much gift wrap will he need to wrap it up?. 5.4 cm. - PowerPoint PPT PresentationTRANSCRIPT
SA = 2llww + 2llhh +2wwhh
SA =2( 5.4 5.4 )( 2.8 2.8 )+ 2( 5.4 5.4 )( 1.5 1.5 )+ 2( 2.8 2.8 )( 1.5 1.5 )
SA = 30.24 + 16.2 + 8.4
SA = SA = 54.84 ≈ 54.8 cm 54.8 cm22 or 54.8 or 54.8 sq cmsq cm
Surface Area of Rectangular Surface Area of Rectangular PrismsPrisms
ExampleExample::
Jeff bought his Jeff bought his mom a box of mom a box of chocolates for chocolates for Mother’s Day Mother’s Day (aww). If the (aww). If the
box is box is rectangular-rectangular-
prism-shaped prism-shaped with a length with a length of 5.4 cm, a of 5.4 cm, a width of 2.8 width of 2.8 cm, and a cm, and a
height of 1.5 height of 1.5 cm, how much cm, how much gift wrap will gift wrap will
he need to he need to wrap it up?wrap it up?
5.4 cm5.4 cm
1.5 1.5 cmcm
2.8 cm2.8 cm
http://greatmathsgames.com/maths/nets/rectangular_prism/rectangular_prism_net.gif
SA= 2SA= 2ππrrhh + 2 + 2 π πrr22
SA= 2( SA= 2( ππ)( )( 0.9 0.9 )( 3.1)( 3.1 ) + 2( ) + 2( ππ)( )( 0.9 0.9 )( )( 0.9 0.9 ) )
SA = 17.53 + 5.09SA = 17.53 + 5.09
SA SA = 22.62 ≈ 22.6 ft≈ 22.6 ft22 or 22.6 or 22.6 sq ftsq ft
Surface Area of CylindersSurface Area of CylindersExampleExample::
Jackie has an Jackie has an old, aluminum old, aluminum garbage can garbage can
that she that she wants to wants to
repaint. If repaint. If the garbage the garbage
can is can is cylinder-cylinder-
shaped, with shaped, with a diameter of a diameter of 1.8 ft and a 1.8 ft and a
height of 3.1 height of 3.1 ft, how much ft, how much paint will she paint will she
need?need?
1.8 ft1.8 ft
3.1
ft
3.1
ft
http://greatmathsgames.com/maths/nets/cylinder/cylinder_sm.gif
V = V = llwwhh
V =(V =(1.2 1.2 )( )( 1.2 1.2 ))( ( 1.2 1.2 ) )
Volume of Rectangular PrismsVolume of Rectangular PrismsExampleExample::
Bud has a Bud has a cube-cube-
shaped shaped container container
that he fills that he fills with with
compost. If compost. If the the
container’s container’s length is length is
1.2 m long, 1.2 m long, how much how much compost compost
will it take will it take to fill it up?to fill it up?
1.2 m1.2 m1.2 m1.2 m
1.2
m1.2
m
V = V = 1.728 ≈ 1.7 m 1.7 m3 3 or 1.7 or 1.7 cubic cubic metersmeters
Vll ww hh
V = V = ππrr2 2 hh
V =(V =( ππ )( )( 0.2 0.2 )( )( 0.20.2 )( )( 1.9 1.9 ) )
Volume of CylindersVolume of CylindersExampleExample::
Wilma has a Wilma has a rain gauge rain gauge
that is that is shaped like shaped like a cylinder. a cylinder. It’s 1.9 yd It’s 1.9 yd
tall and has tall and has a radius of a radius of
0.2 yd. 0.2 yd. What is the What is the capacity of capacity of
Wilma’s Wilma’s rain gauge? rain gauge?
0.2 0.2 ydyd
1.9
yd
1.9
yd
V = 0.238 ≈ 0.2 ydV = 0.238 ≈ 0.2 yd3 3
oror
0.2 cubic 0.2 cubic yardsyards
Changing VolumeChanging VolumeCleveland’s moving, so he’s buying boxes. There’s a Cleveland’s moving, so he’s buying boxes. There’s a smallsmall and a and a extra-largeextra-large. . All dimensions All dimensions (length, width, height) are (length, width, height) are 44 times times longer on the longer on the extra-largeextra-large box. How much more will the box. How much more will the extra-extra-largelarge box hold? box hold?
To find the change in volume, use this To find the change in volume, use this formula:formula:
scale scale factorfactor
( )
Since each dimension is Since each dimension is 44 times bigger, the times bigger, the scale scale factor factor is is 44..
sfsf 44
And, since all And, since all 3 dimensions3 dimensions changed, the changed, the exponentexponent is is 33..
33
44
# of dimensions# of dimensions changedchanged
The extra-large box holds The extra-large box holds 64 times 64 times more than more than the small.the small.
When he compares When he compares the the small small to the to the
medium medium , he finds , he finds only the lengthonly the length is is 4 4 times longertimes longer. How . How much more will the much more will the medium medium box hold?box hold?
4411
6464
The The medium medium
box holds box holds 4 times 4 times
more than more than the small.the small.
1616
When he compares When he compares the the small small to the to the
largelarge, he finds , he finds the the length and widthlength and width
are are 4 times longer4 times longer. . How much more will How much more will the the large large box hold?box hold?
4422The large The large box holds box holds 16 times 16 times
more than more than the small.the small.
Changing Surface AreaChanging Surface AreaFor Valentine’s Day, Neil bought Meg a For Valentine’s Day, Neil bought Meg a littlelittle jewelry box, and a jewelry box, and a huge huge box of box of chocolates. chocolates. All dimensions All dimensions of the of the hugehuge box of chocolates are box of chocolates are 5 times 5 times longer than the longer than the littlelittle jewelry box. How much more wrapping paper will he jewelry box. How much more wrapping paper will he need for the need for the hugehuge box of chocolates? box of chocolates?
To find the change in To find the change in surface areasurface area, use this , use this formula:formula:
scale scale factorfactor
2
Since each dimension is Since each dimension is 55 times bigger, the times bigger, the scale scale factor factor is is 55..
sfsf 55
22
99
The huge box of chocolates needs The huge box of chocolates needs 25 times 25 times more wrapping paper.more wrapping paper.
All the dimensions All the dimensions of large trunk are of large trunk are 3 3 times times longer than a longer than a
small trunk. How small trunk. How much more stain is much more stain is needed to cover the needed to cover the
large trunk?large trunk?
3322
2525The The
large large one one
needsneeds
9 9 timestimes more more stain.stain.
10,0010,0000
All the dimensions of a
big sugar cube are 100 times longer than one grain of sugar. How much more surface does the big one have?
101000
22
22We’ll only solve surface area problems in which all dimensions change
by the same factor. There’s no easy formula
when only 1 or 2 dimensions are changed.
The The large large
one hasone has10,000 10,000 timestimes more more
surface.surface.