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 14144 cm
3 more than that of R.
- What is the height of each block?
- Ian 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
= 19 x 32
= 608 cm
2 Base area of Block S
= 48 x 32
= 1152 cm
2 Base area of Block S more than Block R
= 1152 - 608
= 544 cm
2 Height of each block
= 14144 ÷ 544
= 26 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block R along the length of the box
= 96 ÷ 19
= 5 r 1
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) 26 cm; (b) 15