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 9450 cm
3 more than that of T.
- What is the height of each block?
- Andy packed 8 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
= 19 x 28
= 532 cm
2 Base area of Block U
= 42 x 28
= 882 cm
2 Base area of Block U more than Block T
= 882 - 532
= 350 cm
2 Height of each block
= 9450 ÷ 350
= 27 cm
(b)
Base area of the box
= 8 x 882
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block T along the length of the box
= 84 ÷ 19
= 4 r 8
Number of Block T along the breadth of the box
= 84 ÷ 28
= 3
Number of Block T to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 27 cm; (b) 12