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 520 cm
3 more than that of M.
- What is the height of each block?
- Dylan packed 8 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
= 4 x 8
= 32 cm
2 Base area of Block N
= 12 x 8
= 72 cm
2 Base area of Block N more than Block M
= 72 - 32
= 40 cm
2 Height of each block
= 520 ÷ 40
= 13 cm
(b)
Base area of the box
= 8 x 72
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block M along the length of the box
= 24 ÷ 4
= 6 r 0
Number of Block M along the breadth of the box
= 24 ÷ 8
= 3
Number of Block M to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 13 cm; (b) 18