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 5130 cm
3 more than that of S.
- What is the height of each block?
- Zeph 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
= 12 x 18
= 216 cm
2 Base area of Block T
= 27 x 18
= 486 cm
2 Base area of Block T more than Block S
= 486 - 216
= 270 cm
2 Height of each block
= 5130 ÷ 270
= 19 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block S along the length of the box
= 54 ÷ 12
= 4 r 6
Number of Block S along the breadth of the box
= 54 ÷ 18
= 3
Number of Block S to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 19 cm; (b) 12