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 7680 cm
3 more than that of J.
- What is the height of each block?
- Gabriel 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
= 14 x 20
= 280 cm
2 Base area of Block K
= 30 x 20
= 600 cm
2 Base area of Block K more than Block J
= 600 - 280
= 320 cm
2 Height of each block
= 7680 ÷ 320
= 24 cm
(b)
Base area of the box
= 6 x 600
= 3600 cm
3 Length of the box
= √3600
= 60 cm
Number of Block J along the length of the box
= 60 ÷ 14
= 4 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
= 4 x 3
= 12
Answer(s): (a) 24 cm; (b) 12