PSLE A rectangular block M was cut along the dotted line into two smaller rectangular blocks of equal height, N and P, as shown. The volume of P is 2112 cm
3 more than that of N.
- What is the height of each block?
- Ken packed 6 of block P such that they fit exactly into a box with a square base. The box has the same height as P. At most, how many of block N can be packed into such a box?
(a)
Base area of Block N
= 7 x 12
= 84 cm
2 Base area of Block P
= 18 x 12
= 216 cm
2 Base area of Block P more than Block N
= 216 - 84
= 132 cm
2 Height of each block
= 2112 ÷ 132
= 16 cm
(b)
Base area of the box
= 6 x 216
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block N along the length of the box
= 36 ÷ 7
= 5 r 1
Number of Block N along the breadth of the box
= 36 ÷ 12
= 3
Number of Block N to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 16 cm; (b) 15