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 14742 cm
3 more than that of K.
- What is the height of each block?
- Tim 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
= 12 x 26
= 312 cm
2 Base area of Block L
= 39 x 26
= 1014 cm
2 Base area of Block L more than Block K
= 1014 - 312
= 702 cm
2 Height of each block
= 14742 ÷ 702
= 21 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block K along the length of the box
= 78 ÷ 12
= 6 r 6
Number of Block K along the breadth of the box
= 78 ÷ 26
= 3
Number of Block K to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 21 cm; (b) 18