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 14848 cm
3 more than that of M.
- What is the height of each block?
- Will 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
= 20 x 32
= 640 cm
2 Base area of Block N
= 48 x 32
= 1152 cm
2 Base area of Block N more than Block M
= 1152 - 640
= 512 cm
2 Height of each block
= 14848 ÷ 512
= 29 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block M along the length of the box
= 96 ÷ 20
= 4 r 16
Number of Block M along the breadth of the box
= 96 ÷ 32
= 3
Number of Block M to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 29 cm; (b) 12