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 6480 cm
3 more than that of R.
- What is the height of each block?
- Oliver packed 8 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
= 17 x 24
= 408 cm
2 Base area of Block S
= 36 x 24
= 648 cm
2 Base area of Block S more than Block R
= 648 - 408
= 240 cm
2 Height of each block
= 6480 ÷ 240
= 27 cm
(b)
Base area of the box
= 8 x 648
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block R along the length of the box
= 72 ÷ 17
= 4 r 4
Number of Block R along the breadth of the box
= 72 ÷ 24
= 3
Number of Block R to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 27 cm; (b) 12