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.