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 1296 cm
3 more than that of W.
- What is the height of each block?
- David 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
= 6 x 12
= 72 cm
2 Base area of Block X
= 18 x 12
= 216 cm
2 Base area of Block X more than Block W
= 216 - 72
= 144 cm
2 Height of each block
= 1296 ÷ 144
= 9 cm
(b)
Base area of the box
= 6 x 216
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block W along the length of the box
= 36 ÷ 6
= 6 r 0
Number of Block W along the breadth of the box
= 36 ÷ 12
= 3
Number of Block W to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 9 cm; (b) 18