PSLE A rectangular block H was cut along the dotted line into two smaller rectangular blocks of equal height, J and K, as shown. The volume of K is 5220 cm
3 more than that of J.
- What is the height of each block?
- Zeph packed 8 of block K such that they fit exactly into a box with a square base. The box has the same height as K. At most, how many of block J can be packed into such a box?
(a)
Base area of Block J
= 8 x 20
= 160 cm
2 Base area of Block K
= 30 x 20
= 450 cm
2 Base area of Block K more than Block J
= 450 - 160
= 290 cm
2 Height of each block
= 5220 ÷ 290
= 18 cm
(b)
Base area of the box
= 8 x 450
= 3600 cm
3 Length of the box
= √3600
= 60 cm
Number of Block J along the length of the box
= 60 ÷ 8
= 7 r 4
Number of Block J along the breadth of the box
= 60 ÷ 20
= 3
Number of Block J to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 18 cm; (b) 21