PSLE A rectangular block V was cut along the dotted line into two smaller rectangular blocks of equal height, W and X, as shown. The volume of X is 23040 cm
3 more than that of W.
- What is the height of each block?
- Jack packed 6 of block X such that they fit exactly into a box with a square base. The box has the same height as X. At most, how many of block W can be packed into such a box?
(a)
Base area of Block W
= 18 x 32
= 576 cm
2 Base area of Block X
= 48 x 32
= 1536 cm
2 Base area of Block X more than Block W
= 1536 - 576
= 960 cm
2 Height of each block
= 23040 ÷ 960
= 24 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block W along the length of the box
= 96 ÷ 18
= 5 r 6
Number of Block W along the breadth of the box
= 96 ÷ 32
= 3
Number of Block W to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 24 cm; (b) 15