PSLE A rectangular block E was cut along the dotted line into two smaller rectangular blocks of equal height, F and G, as shown. The volume of G is 320 cm
3 more than that of F.
- What is the height of each block?
- Zeph packed 8 of block G such that they fit exactly into a box with a square base. The box has the same height as G. At most, how many of block F can be packed into such a box?
(a)
Base area of Block F
= 5 x 8
= 40 cm
2 Base area of Block G
= 12 x 8
= 72 cm
2 Base area of Block G more than Block F
= 72 - 40
= 32 cm
2 Height of each block
= 320 ÷ 32
= 10 cm
(b)
Base area of the box
= 8 x 72
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block F along the length of the box
= 24 ÷ 5
= 4 r 4
Number of Block F along the breadth of the box
= 24 ÷ 8
= 3
Number of Block F to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 10 cm; (b) 12