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 1000 cm
3 more than that of J.
- What is the height of each block?
- Michael packed 6 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
= 5 x 10
= 50 cm
2 Base area of Block K
= 15 x 10
= 150 cm
2 Base area of Block K more than Block J
= 150 - 50
= 100 cm
2 Height of each block
= 1000 ÷ 100
= 10 cm
(b)
Base area of the box
= 6 x 150
= 900 cm
3 Length of the box
= √900
= 30 cm
Number of Block J along the length of the box
= 30 ÷ 5
= 6 r 0
Number of Block J along the breadth of the box
= 30 ÷ 10
= 3
Number of Block J to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 10 cm; (b) 18