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 21120 cm
3 more than that of R.
- What is the height of each block?
- Ahmad 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
= 18 x 32
= 576 cm
2 Base area of Block S
= 48 x 32
= 1536 cm
2 Base area of Block S more than Block R
= 1536 - 576
= 960 cm
2 Height of each block
= 21120 ÷ 960
= 22 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block R along the length of the box
= 96 ÷ 18
= 5 r 6
Number of Block R along the breadth of the box
= 96 ÷ 32
= 3
Number of Block R to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 22 cm; (b) 15