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 2940 cm
3 more than that of X.
- What is the height of each block?
- Carl 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
= 6 x 14
= 84 cm
2 Base area of Block Y
= 21 x 14
= 294 cm
2 Base area of Block Y more than Block X
= 294 - 84
= 210 cm
2 Height of each block
= 2940 ÷ 210
= 14 cm
(b)
Base area of the box
= 6 x 294
= 1764 cm
3 Length of the box
= √1764
= 42 cm
Number of Block X along the length of the box
= 42 ÷ 6
= 7 r 0
Number of Block X along the breadth of the box
= 42 ÷ 14
= 3
Number of Block X to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 14 cm; (b) 21