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 5712 cm
3 more than that of J.
- What is the height of each block?
- Ahmad packed 8 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
= 10 x 24
= 240 cm
2 Base area of Block K
= 36 x 24
= 648 cm
2 Base area of Block K more than Block J
= 648 - 240
= 408 cm
2 Height of each block
= 5712 ÷ 408
= 14 cm
(b)
Base area of the box
= 8 x 648
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block J along the length of the box
= 72 ÷ 10
= 7 r 2
Number of Block J along the breadth of the box
= 72 ÷ 24
= 3
Number of Block J to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 14 cm; (b) 21