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 8806 cm
3 more than that of X.
- What is the height of each block?
- Dylan 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
= 13 x 28
= 364 cm
2 Base area of Block Y
= 42 x 28
= 882 cm
2 Base area of Block Y more than Block X
= 882 - 364
= 518 cm
2 Height of each block
= 8806 ÷ 518
= 17 cm
(b)
Base area of the box
= 8 x 882
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block X along the length of the box
= 84 ÷ 13
= 6 r 6
Number of Block X along the breadth of the box
= 84 ÷ 28
= 3
Number of Block X to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 17 cm; (b) 18