PSLE A rectangular block L was cut along the dotted line into two smaller rectangular blocks of equal height, M and N, as shown. The volume of N is 9108 cm
3 more than that of M.
- What is the height of each block?
- Liam packed 6 of block N such that they fit exactly into a box with a square base. The box has the same height as N. At most, how many of block M can be packed into such a box?
(a)
Base area of Block M
= 15 x 22
= 330 cm
2 Base area of Block N
= 33 x 22
= 726 cm
2 Base area of Block N more than Block M
= 726 - 330
= 396 cm
2 Height of each block
= 9108 ÷ 396
= 23 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block M along the length of the box
= 66 ÷ 15
= 4 r 6
Number of Block M along the breadth of the box
= 66 ÷ 22
= 3
Number of Block M to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 23 cm; (b) 12