PSLE A rectangular block K was cut along the dotted line into two smaller rectangular blocks of equal height, L and M, as shown. The volume of M is 11648 cm
3 more than that of L.
- What is the height of each block?
- Michael packed 6 of block M such that they fit exactly into a box with a square base. The box has the same height as M. At most, how many of block L can be packed into such a box?
(a)
Base area of Block L
= 11 x 26
= 286 cm
2 Base area of Block M
= 39 x 26
= 1014 cm
2 Base area of Block M more than Block L
= 1014 - 286
= 728 cm
2 Height of each block
= 11648 ÷ 728
= 16 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block L along the length of the box
= 78 ÷ 11
= 7 r 1
Number of Block L along the breadth of the box
= 78 ÷ 26
= 3
Number of Block L to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 16 cm; (b) 21