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 11040 cm
3 more than that of M.
- What is the height of each block?
- Charlie 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
= 13 x 24
= 312 cm
2 Base area of Block N
= 36 x 24
= 864 cm
2 Base area of Block N more than Block M
= 864 - 312
= 552 cm
2 Height of each block
= 11040 ÷ 552
= 20 cm
(b)
Base area of the box
= 6 x 864
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block M along the length of the box
= 72 ÷ 13
= 5 r 7
Number of Block M along the breadth of the box
= 72 ÷ 24
= 3
Number of Block M to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 20 cm; (b) 15