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 360 cm
3 more than that of J.
- What is the height of each block?
- David 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
= 4 x 8
= 32 cm
2 Base area of Block K
= 12 x 8
= 72 cm
2 Base area of Block K more than Block J
= 72 - 32
= 40 cm
2 Height of each block
= 360 ÷ 40
= 9 cm
(b)
Base area of the box
= 8 x 72
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block J along the length of the box
= 24 ÷ 4
= 6 r 0
Number of Block J along the breadth of the box
= 24 ÷ 8
= 3
Number of Block J to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 9 cm; (b) 18