PSLE A rectangular block W was cut along the dotted line into two smaller rectangular blocks of equal height, X and Y, as shown. The volume of Y is 144 cm
3 more than that of X.
- What is the height of each block?
- Fred packed 6 of block Y such that they fit exactly into a box with a square base. The box has the same height as Y. At most, how many of block X can be packed into such a box?
(a)
Base area of Block X
= 2 x 4
= 8 cm
2 Base area of Block Y
= 6 x 4
= 24 cm
2 Base area of Block Y more than Block X
= 24 - 8
= 16 cm
2 Height of each block
= 144 ÷ 16
= 9 cm
(b)
Base area of the box
= 6 x 24
= 144 cm
3 Length of the box
= √144
= 12 cm
Number of Block X along the length of the box
= 12 ÷ 2
= 6 r 0
Number of Block X along the breadth of the box
= 12 ÷ 4
= 3
Number of Block X to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 9 cm; (b) 18