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 810 cm
3 more than that of P.
- What is the height of each block?
- Billy 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
= 6 x 12
= 72 cm
2 Base area of Block Q
= 18 x 12
= 162 cm
2 Base area of Block Q more than Block P
= 162 - 72
= 90 cm
2 Height of each block
= 810 ÷ 90
= 9 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block P along the length of the box
= 36 ÷ 6
= 6 r 0
Number of Block P along the breadth of the box
= 36 ÷ 12
= 3
Number of Block P to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 9 cm; (b) 18