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 1428 cm
3 more than that of R.
- What is the height of each block?
- Oscar 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
= 5 x 12
= 60 cm
2 Base area of Block S
= 18 x 12
= 162 cm
2 Base area of Block S more than Block R
= 162 - 60
= 102 cm
2 Height of each block
= 1428 ÷ 102
= 14 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block R along the length of the box
= 36 ÷ 5
= 7 r 1
Number of Block R along the breadth of the box
= 36 ÷ 12
= 3
Number of Block R to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 14 cm; (b) 21