PSLE A rectangular block H was cut along the dotted line into two smaller rectangular blocks of equal height, J and K, as shown. The volume of K is 20800 cm
3 more than that of J.
- What is the height of each block?
- Tim packed 6 of block K such that they fit exactly into a box with a square base. The box has the same height as K. At most, how many of block J can be packed into such a box?
(a)
Base area of Block J
= 22 x 32
= 704 cm
2 Base area of Block K
= 48 x 32
= 1536 cm
2 Base area of Block K more than Block J
= 1536 - 704
= 832 cm
2 Height of each block
= 20800 ÷ 832
= 25 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block J along the length of the box
= 96 ÷ 22
= 4 r 8
Number of Block J along the breadth of the box
= 96 ÷ 32
= 3
Number of Block J to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 25 cm; (b) 12