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 5832 cm
3 more than that of M.
- What is the height of each block?
- Ian 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
= 9 x 18
= 162 cm
2 Base area of Block N
= 27 x 18
= 486 cm
2 Base area of Block N more than Block M
= 486 - 162
= 324 cm
2 Height of each block
= 5832 ÷ 324
= 18 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block M along the length of the box
= 54 ÷ 9
= 6 r 0
Number of Block M along the breadth of the box
= 54 ÷ 18
= 3
Number of Block M to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 18 cm; (b) 18