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 810 cm
3 more than that of T.
- What is the height of each block?
- George 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
= 6 x 10
= 60 cm
2 Base area of Block U
= 15 x 10
= 150 cm
2 Base area of Block U more than Block T
= 150 - 60
= 90 cm
2 Height of each block
= 810 ÷ 90
= 9 cm
(b)
Base area of the box
= 6 x 150
= 900 cm
3 Length of the box
= √900
= 30 cm
Number of Block T along the length of the box
= 30 ÷ 6
= 5 r 0
Number of Block T along the breadth of the box
= 30 ÷ 10
= 3
Number of Block T to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 9 cm; (b) 15