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 15548 cm
3 more than that of X.
- What is the height of each block?
- Jack 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
= 16 x 26
= 416 cm
2 Base area of Block Y
= 39 x 26
= 1014 cm
2 Base area of Block Y more than Block X
= 1014 - 416
= 598 cm
2 Height of each block
= 15548 ÷ 598
= 26 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block X along the length of the box
= 78 ÷ 16
= 4 r 14
Number of Block X along the breadth of the box
= 78 ÷ 26
= 3
Number of Block X to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 26 cm; (b) 12