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 7140 cm
3 more than that of P.
- What is the height of each block?
- Dylan packed 6 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
= 9 x 20
= 180 cm
2 Base area of Block Q
= 30 x 20
= 600 cm
2 Base area of Block Q more than Block P
= 600 - 180
= 420 cm
2 Height of each block
= 7140 ÷ 420
= 17 cm
(b)
Base area of the box
= 6 x 600
= 3600 cm
3 Length of the box
= √3600
= 60 cm
Number of Block P along the length of the box
= 60 ÷ 9
= 6 r 6
Number of Block P along the breadth of the box
= 60 ÷ 20
= 3
Number of Block P to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 17 cm; (b) 18