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 1170 cm
3 more than that of S.
- What is the height of each block?
- Flynn packed 8 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
= 7 x 12
= 84 cm
2 Base area of Block T
= 18 x 12
= 162 cm
2 Base area of Block T more than Block S
= 162 - 84
= 78 cm
2 Height of each block
= 1170 ÷ 78
= 15 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block S along the length of the box
= 36 ÷ 7
= 5 r 1
Number of Block S along the breadth of the box
= 36 ÷ 12
= 3
Number of Block S to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 15 cm; (b) 15