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 1760 cm
3 more than that of N.
- What is the height of each block?
- Ahmad packed 8 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
= 8 x 16
= 128 cm
2 Base area of Block P
= 24 x 16
= 288 cm
2 Base area of Block P more than Block N
= 288 - 128
= 160 cm
2 Height of each block
= 1760 ÷ 160
= 11 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block N along the length of the box
= 48 ÷ 8
= 6 r 0
Number of Block N along the breadth of the box
= 48 ÷ 16
= 3
Number of Block N to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 11 cm; (b) 18