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 140 cm
3 more than that of X.
- What is the height of each block?
- Howard packed 8 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
= 1 x 4
= 4 cm
2 Base area of Block Y
= 6 x 4
= 18 cm
2 Base area of Block Y more than Block X
= 18 - 4
= 14 cm
2 Height of each block
= 140 ÷ 14
= 10 cm
(b)
Base area of the box
= 8 x 18
= 144 cm
3 Length of the box
= √144
= 12 cm
Number of Block X along the length of the box
= 12 ÷ 1
= 12 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
= 12 x 3
= 36
Answer(s): (a) 10 cm; (b) 36