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 21600 cm
3 more than that of L.
- What is the height of each block?
- Ken 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
= 21 x 32
= 672 cm
2 Base area of Block M
= 48 x 32
= 1536 cm
2 Base area of Block M more than Block L
= 1536 - 672
= 864 cm
2 Height of each block
= 21600 ÷ 864
= 25 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block L along the length of the box
= 96 ÷ 21
= 4 r 12
Number of Block L along the breadth of the box
= 96 ÷ 32
= 3
Number of Block L to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 25 cm; (b) 12