PSLE A rectangular block N was cut along the dotted line into two smaller rectangular blocks of equal height, P and Q, as shown. The volume of Q is 256 cm
3 more than that of P.
- What is the height of each block?
- Fred packed 8 of block Q such that they fit exactly into a box with a square base. The box has the same height as Q. At most, how many of block P can be packed into such a box?
(a)
Base area of Block P
= 5 x 8
= 40 cm
2 Base area of Block Q
= 12 x 8
= 72 cm
2 Base area of Block Q more than Block P
= 72 - 40
= 32 cm
2 Height of each block
= 256 ÷ 32
= 8 cm
(b)
Base area of the box
= 8 x 72
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block P along the length of the box
= 24 ÷ 5
= 4 r 4
Number of Block P along the breadth of the box
= 24 ÷ 8
= 3
Number of Block P to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 8 cm; (b) 12