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 21840 cm
3 more than that of J.
- What is the height of each block?
- Warren 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
= 17 x 30
= 510 cm
2 Base area of Block K
= 45 x 30
= 1350 cm
2 Base area of Block K more than Block J
= 1350 - 510
= 840 cm
2 Height of each block
= 21840 ÷ 840
= 26 cm
(b)
Base area of the box
= 6 x 1350
= 8100 cm
3 Length of the box
= √8100
= 90 cm
Number of Block J along the length of the box
= 90 ÷ 17
= 5 r 5
Number of Block J along the breadth of the box
= 90 ÷ 30
= 3
Number of Block J to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 26 cm; (b) 15