PSLE A rectangular block G was cut along the dotted line into two smaller rectangular blocks of equal height, H and J, as shown. The volume of J is 448 cm
3 more than that of H.
- What is the height of each block?
- Wesley packed 6 of block J such that they fit exactly into a box with a square base. The box has the same height as J. At most, how many of block H can be packed into such a box?
(a)
Base area of Block H
= 4 x 8
= 32 cm
2 Base area of Block J
= 12 x 8
= 96 cm
2 Base area of Block J more than Block H
= 96 - 32
= 64 cm
2 Height of each block
= 448 ÷ 64
= 7 cm
(b)
Base area of the box
= 6 x 96
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block H along the length of the box
= 24 ÷ 4
= 6 r 0
Number of Block H along the breadth of the box
= 24 ÷ 8
= 3
Number of Block H to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 7 cm; (b) 18