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 18496 cm
3 more than that of F.
- What is the height of each block?
- Vincent packed 6 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
= 14 x 32
= 448 cm
2 Base area of Block G
= 48 x 32
= 1536 cm
2 Base area of Block G more than Block F
= 1536 - 448
= 1088 cm
2 Height of each block
= 18496 ÷ 1088
= 17 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block F along the length of the box
= 96 ÷ 14
= 6 r 12
Number of Block F along the breadth of the box
= 96 ÷ 32
= 3
Number of Block F to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 17 cm; (b) 18