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 5472 cm
3 more than that of H.
- What is the height of each block?
- Elijah 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
= 11 x 18
= 198 cm
2 Base area of Block J
= 27 x 18
= 486 cm
2 Base area of Block J more than Block H
= 486 - 198
= 288 cm
2 Height of each block
= 5472 ÷ 288
= 19 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block H along the length of the box
= 54 ÷ 11
= 4 r 10
Number of Block H along the breadth of the box
= 54 ÷ 18
= 3
Number of Block H to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 19 cm; (b) 12