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 12584 cm
3 more than that of M.
- What is the height of each block?
- George 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
= 17 x 26
= 442 cm
2 Base area of Block N
= 39 x 26
= 1014 cm
2 Base area of Block N more than Block M
= 1014 - 442
= 572 cm
2 Height of each block
= 12584 ÷ 572
= 22 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block M along the length of the box
= 78 ÷ 17
= 4 r 10
Number of Block M along the breadth of the box
= 78 ÷ 26
= 3
Number of Block M to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 22 cm; (b) 12