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 13984 cm
3 more than that of H.
- What is the height of each block?
- Tim packed 8 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
= 17 x 32
= 544 cm
2 Base area of Block J
= 48 x 32
= 1152 cm
2 Base area of Block J more than Block H
= 1152 - 544
= 608 cm
2 Height of each block
= 13984 ÷ 608
= 23 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block H along the length of the box
= 96 ÷ 17
= 5 r 11
Number of Block H along the breadth of the box
= 96 ÷ 32
= 3
Number of Block H to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 23 cm; (b) 15