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 9384 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
= 13 x 24
= 312 cm
2 Base area of Block U
= 36 x 24
= 864 cm
2 Base area of Block U more than Block T
= 864 - 312
= 552 cm
2 Height of each block
= 9384 ÷ 552
= 17 cm
(b)
Base area of the box
= 6 x 864
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block T along the length of the box
= 72 ÷ 13
= 5 r 7
Number of Block T along the breadth of the box
= 72 ÷ 24
= 3
Number of Block T to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 17 cm; (b) 15