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• More packing problems •••
Show any workings-out for this page.
UJ The toy shop owner completely filled a storage box, ~=M•l&10--
measuring 12 cm by 12 cm by 12 cm, with dice.
Each dice has an edge length of 3 cm. PAGE 71
Work out how many dice were stored in the box.
~ The shop also sells giant dice with edges twice as long.
a Decide if the same box can be exactly filled
with the giant dice, and explain why.
b Work out how many giant dice will fit in the box.
@] The store has 24 Jack-in-the-boxes,
each in a cube with an edge length of 5 cm.
They are kept in a troy 20 cm wide and 30 cm long.
Work out if all the Jack-in-the-boxes will fit
in o single loyer in the troy.
W Packs of Happy Family cards
ore 10cm by 6cm by 2cm.
CHALLENGE
• If the height of o cuboid is halved,
what must be done to the other dimensions
so that the volume stays the same?
• Show how you decide.
DJ DJ
4 dice along the length x 4 dice along the breadth x 4 dice along the height a Edge length of cube = 3 cm
= 64 dice Volume in cubes = 3 x 3 x 3 = 27 = 3 3
b Open: write similar statements for four other cubes.
a Yes, because you can exactly fit two dice along the length, breadth and
height of the box.
b 2 dices along the length x 2 dice along the breadth x 2 dice along the a no b no c yes d yes e no f no g yes h yes
height = 8 dice
~ Challenge
1 small cube has no faces painted.
Challenge a 216 b 343 c 512 d 72Q
6 small cubes are painted on 1 face.
4 boxes along the width x 6 boxes If the height of a cuboid is halved 12 small cubes are painted on 2 faces.
along the length= 24 boxes either the length or the breadth 8 small cubes are painted on 3 faces.
must be doubled so that the volume O small cubes are painted on 4 faces.
stays the same.
Open: try different sized cubes.
3 packs along the length x 2 packs
along the breadth x 2 packs along
the height = 12 packs
