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 1014 cm
3 more than that of M.
- What is the height of each block?
- Zane 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
= 7 x 12
= 84 cm
2 Base area of Block N
= 18 x 12
= 162 cm
2 Base area of Block N more than Block M
= 162 - 84
= 78 cm
2 Height of each block
= 1014 ÷ 78
= 13 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block M along the length of the box
= 36 ÷ 7
= 5 r 1
Number of Block M along the breadth of the box
= 36 ÷ 12
= 3
Number of Block M to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 13 cm; (b) 15