PSLE A rectangular block Q was cut along the dotted line into two smaller rectangular blocks of equal height, R and S, as shown. The volume of S is 8228 cm
3 more than that of R.
- What is the height of each block?
- Vincent packed 6 of block S such that they fit exactly into a box with a square base. The box has the same height as S. At most, how many of block R can be packed into such a box?
(a)
Base area of Block R
= 11 x 22
= 242 cm
2 Base area of Block S
= 33 x 22
= 726 cm
2 Base area of Block S more than Block R
= 726 - 242
= 484 cm
2 Height of each block
= 8228 ÷ 484
= 17 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block R along the length of the box
= 66 ÷ 11
= 6 r 0
Number of Block R along the breadth of the box
= 66 ÷ 22
= 3
Number of Block R to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 17 cm; (b) 18