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 3094 cm
3 more than that of J.
- What is the height of each block?
- Valen 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
= 8 x 14
= 112 cm
2 Base area of Block K
= 21 x 14
= 294 cm
2 Base area of Block K more than Block J
= 294 - 112
= 182 cm
2 Height of each block
= 3094 ÷ 182
= 17 cm
(b)
Base area of the box
= 6 x 294
= 1764 cm
3 Length of the box
= √1764
= 42 cm
Number of Block J along the length of the box
= 42 ÷ 8
= 5 r 2
Number of Block J along the breadth of the box
= 42 ÷ 14
= 3
Number of Block J to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 17 cm; (b) 15