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 1792 cm
3 more than that of M.
- What is the height of each block?
- Riordan 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
= 10 x 16
= 160 cm
2 Base area of Block N
= 24 x 16
= 288 cm
2 Base area of Block N more than Block M
= 288 - 160
= 128 cm
2 Height of each block
= 1792 ÷ 128
= 14 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block M along the length of the box
= 48 ÷ 10
= 4 r 8
Number of Block M along the breadth of the box
= 48 ÷ 16
= 3
Number of Block M to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 14 cm; (b) 12