PSLE A rectangular block T was cut along the dotted line into two smaller rectangular blocks of equal height, U and V, as shown. The volume of V is 2016 cm
3 more than that of U.
- What is the height of each block?
- Asher packed 6 of block V such that they fit exactly into a box with a square base. The box has the same height as V. At most, how many of block U can be packed into such a box?
(a)
Base area of Block U
= 6 x 12
= 72 cm
2 Base area of Block V
= 18 x 12
= 216 cm
2 Base area of Block V more than Block U
= 216 - 72
= 144 cm
2 Height of each block
= 2016 ÷ 144
= 14 cm
(b)
Base area of the box
= 6 x 216
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block U along the length of the box
= 36 ÷ 6
= 6 r 0
Number of Block U along the breadth of the box
= 36 ÷ 12
= 3
Number of Block U to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 14 cm; (b) 18