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 3136 cm
3 more than that of R.
- What is the height of each block?
- Luis 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
= 7 x 14
= 98 cm
2 Base area of Block S
= 21 x 14
= 294 cm
2 Base area of Block S more than Block R
= 294 - 98
= 196 cm
2 Height of each block
= 3136 ÷ 196
= 16 cm
(b)
Base area of the box
= 6 x 294
= 1764 cm
3 Length of the box
= √1764
= 42 cm
Number of Block R along the length of the box
= 42 ÷ 7
= 6 r 0
Number of Block R along the breadth of the box
= 42 ÷ 14
= 3
Number of Block R to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 16 cm; (b) 18