PSLE A rectangular block S was cut along the dotted line into two smaller rectangular blocks of equal height, T and U, as shown. The volume of U is 4624 cm
3 more than that of T.
- What is the height of each block?
- Ken packed 6 of block U such that they fit exactly into a box with a square base. The box has the same height as U. At most, how many of block T can be packed into such a box?
(a)
Base area of Block T
= 7 x 16
= 112 cm
2 Base area of Block U
= 24 x 16
= 384 cm
2 Base area of Block U more than Block T
= 384 - 112
= 272 cm
2 Height of each block
= 4624 ÷ 272
= 17 cm
(b)
Base area of the box
= 6 x 384
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block T along the length of the box
= 48 ÷ 7
= 6 r 6
Number of Block T along the breadth of the box
= 48 ÷ 16
= 3
Number of Block T to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 17 cm; (b) 18