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 1920 cm
3 more than that of X.
- What is the height of each block?
- Liam 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
= 8 x 16
= 128 cm
2 Base area of Block Y
= 24 x 16
= 288 cm
2 Base area of Block Y more than Block X
= 288 - 128
= 160 cm
2 Height of each block
= 1920 ÷ 160
= 12 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block X along the length of the box
= 48 ÷ 8
= 6 r 0
Number of Block X along the breadth of the box
= 48 ÷ 16
= 3
Number of Block X to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 12 cm; (b) 18