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 1936 cm
3 more than that of H.
- What is the height of each block?
- Pierre 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
= 7 x 16
= 112 cm
2 Base area of Block J
= 24 x 16
= 288 cm
2 Base area of Block J more than Block H
= 288 - 112
= 176 cm
2 Height of each block
= 1936 ÷ 176
= 11 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block H along the length of the box
= 48 ÷ 7
= 6 r 6
Number of Block H along the breadth of the box
= 48 ÷ 16
= 3
Number of Block H to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 11 cm; (b) 18