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 7084 cm
3 more than that of K.
- What is the height of each block?
- Vaidev packed 6 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
= 10 x 22
= 220 cm
2 Base area of Block L
= 33 x 22
= 726 cm
2 Base area of Block L more than Block K
= 726 - 220
= 506 cm
2 Height of each block
= 7084 ÷ 506
= 14 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block K along the length of the box
= 66 ÷ 10
= 6 r 6
Number of Block K along the breadth of the box
= 66 ÷ 22
= 3
Number of Block K to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 14 cm; (b) 18