Page 37 - 01-Yr5_Front cover-ccp.indd

m Packing problems m m m I centicubes j
• Cuboid volume • • • R • •
You might like to use Centicubes or other materials
You know that a quick way to find the volume of any cuboid is like this·
or draw diagrams to help you with.this page.
Volume -= length x breadth x height or V = Ix b x h.
{You might prefer to use the word 'width' instead of 'breadth'.)
QJ Copy and complete this equation QJ Rachel has an empty box 2 cm by 3 cm by 4 cm.
for this cuboid made of Centicubes.
V= t xbxh
= .. . cm x 2 cm x 3 cm She has also mode several cuboids like these.
= ... cm3
0 Write about these cuboids in the same way.
a Describe what combination of cuboids Rachel could use to fill her box.
b Try to find another way to fill the box.
! I
·~I! @] Rob has four cuboids like A, one cuboid like B
1 I and one cuboid like C .
..\.
Volume of cuboid
rn Find the missing dimensions v
for each cuboid on this table. a Scm 2cm 2cm
Record your answers like this. cuboid C
Scm 4cm 80 cm 3 cuboid B
cuboid A
a V= 20 cm3
c 6cm 1cm 72 cm3
a Find the volume of each type of cuboid.
d 4cm 3crn 60cm3 b Find the total volume of all his cuboids.
/CHALLENGE ""'
4cm 3crn 84cm3 [TI Rob needs to pack the six cuboids into a box exactly the right size.
• A cuboid has a volume of 120cm3. f Scm 3cm 4cm
• If one dimension is 5 cm, find as a Write what dimensions Rob's box should hove.
many possibilities as you con g 4cm 4cm 64cm3 b Could the box hove other dimensions and still be the right size?
for the other two dimensions
\. ~ 2cm 7cm 98cm' Now try page 70.
m ISTEPS 5:17 1
rn Challenge rn
V=lxbxh 5 cm x 1 cm x 24 cm = 120cm 3 a - b Possible combinations:
= 4 cm x 2 cm x 3 cm 5cm x 2cm x 12cm = 120cm 3 12 of the 2 x 1x1 cuboids;
= 24 cm 3 5cm x 3cm x Bern = 120cm 3 10 of the 2 x 1x1cuboids+1 of the 2 x 2 x 1 cuboids;
5cm x 4cm x 6cm = 120cm 3 8 of the 2 x 1 x 1 cuboids + 2 of the 2 x 2 x 1 cuboids;
6 of the 2 x 1 x 1 cuboids + 3 of the 2 x 2 x 1 cuboids;
4 of the 2 x 1 x 1 cuboids + 4 of the 2 x 2 x 1 cuboids;
a 6cm x 4cm x 4cm = q6cm 3 2 of the 2 x 1 x 1 cuboids + 5 of the 2 x 2 x 1 cuboids;
6 of the 2 x 2 x 1 cuboids.
b 4cm x 5cm x 6cm = 120cm 3
~
c 3cm x 5cm x 4cm = 60cm 3
~ a Cuboid A= 2cm x 2cm x 3cm = 12cm 3 a Any of these dimensions:
18cm x 2cm x 2cm
3
Cuboid B = 2cm x 2cm x 2cm = 8cm
a V= 20cm 3 b I= 4cm Cuboid C = 2cm x 2cm x 4cm = 16cm 3 qcm x 4cm x 2cm
6cm x 6cm x 2cm
3
3
3
c b = 12cm d h= 5cm b 4 x 1 2 cm + 8 cm + 16 cm = 72 cm 3
b Yes (but they won't fit in
e I= ?cm f V= q6cm 3 the box if any of the
dimensions are 3 cm or
g b= 4cm h I= 7cm
1 cm).