PSLE A rectangular block R was cut along the dotted line into two smaller rectangular blocks of equal height, S and T, as shown. The volume of T is 378 cm
3 more than that of S.
- What is the height of each block?
- Japheth packed 6 of block T such that they fit exactly into a box with a square base. The box has the same height as T. At most, how many of block S can be packed into such a box?
(a)
Base area of Block S
= 2 x 6
= 12 cm
2 Base area of Block T
= 9 x 6
= 54 cm
2 Base area of Block T more than Block S
= 54 - 12
= 42 cm
2 Height of each block
= 378 ÷ 42
= 9 cm
(b)
Base area of the box
= 6 x 54
= 324 cm
3 Length of the box
= √324
= 18 cm
Number of Block S along the length of the box
= 18 ÷ 2
= 9 r 0
Number of Block S along the breadth of the box
= 18 ÷ 6
= 3
Number of Block S to pack into the box at most
= 9 x 3
= 27
Answer(s): (a) 9 cm; (b) 27