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 14560 cm
3 more than that of R.
- What is the height of each block?
- Seth 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 26
= 286 cm
2 Base area of Block S
= 39 x 26
= 1014 cm
2 Base area of Block S more than Block R
= 1014 - 286
= 728 cm
2 Height of each block
= 14560 ÷ 728
= 20 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block R along the length of the box
= 78 ÷ 11
= 7 r 1
Number of Block R along the breadth of the box
= 78 ÷ 26
= 3
Number of Block R to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 20 cm; (b) 21