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 21632 cm
3 more than that of M.
- What is the height of each block?
- Gabriel 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
= 22 x 32
= 704 cm
2 Base area of Block N
= 48 x 32
= 1536 cm
2 Base area of Block N more than Block M
= 1536 - 704
= 832 cm
2 Height of each block
= 21632 ÷ 832
= 26 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block M along the length of the box
= 96 ÷ 22
= 4 r 8
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) 26 cm; (b) 12