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 13440 cm
3 more than that of T.
- What is the height of each block?
- Xavier 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
= 21 x 32
= 672 cm
2 Base area of Block U
= 48 x 32
= 1152 cm
2 Base area of Block U more than Block T
= 1152 - 672
= 480 cm
2 Height of each block
= 13440 ÷ 480
= 28 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block T along the length of the box
= 96 ÷ 21
= 4 r 12
Number of Block T along the breadth of the box
= 96 ÷ 32
= 3
Number of Block T to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 28 cm; (b) 12