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 990 cm
3 more than that of T.
- What is the height of each block?
- Mark 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
= 8 x 12
= 96 cm
2 Base area of Block U
= 18 x 12
= 162 cm
2 Base area of Block U more than Block T
= 162 - 96
= 66 cm
2 Height of each block
= 990 ÷ 66
= 15 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block T along the length of the box
= 36 ÷ 8
= 4 r 4
Number of Block T along the breadth of the box
= 36 ÷ 12
= 3
Number of Block T to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 15 cm; (b) 12