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 8064 cm
3 more than that of S.
- What is the height of each block?
- Jack 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
= 11 x 24
= 264 cm
2 Base area of Block T
= 36 x 24
= 648 cm
2 Base area of Block T more than Block S
= 648 - 264
= 384 cm
2 Height of each block
= 8064 ÷ 384
= 21 cm
(b)
Base area of the box
= 8 x 648
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block S along the length of the box
= 72 ÷ 11
= 6 r 6
Number of Block S along the breadth of the box
= 72 ÷ 24
= 3
Number of Block S to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 21 cm; (b) 18