PSLE A rectangular block J was cut along the dotted line into two smaller rectangular blocks of equal height, K and L, as shown. The volume of L is 256 cm
3 more than that of K.
- What is the height of each block?
- Howard packed 8 of block L such that they fit exactly into a box with a square base. The box has the same height as L. At most, how many of block K can be packed into such a box?
(a)
Base area of Block K
= 5 x 8
= 40 cm
2 Base area of Block L
= 12 x 8
= 72 cm
2 Base area of Block L more than Block K
= 72 - 40
= 32 cm
2 Height of each block
= 256 ÷ 32
= 8 cm
(b)
Base area of the box
= 8 x 72
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block K along the length of the box
= 24 ÷ 5
= 4 r 4
Number of Block K along the breadth of the box
= 24 ÷ 8
= 3
Number of Block K to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 8 cm; (b) 12