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 13824 cm
3 more than that of P.
- What is the height of each block?
- Jack 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
= 18 x 32
= 576 cm
2 Base area of Block Q
= 48 x 32
= 1152 cm
2 Base area of Block Q more than Block P
= 1152 - 576
= 576 cm
2 Height of each block
= 13824 ÷ 576
= 24 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block P along the length of the box
= 96 ÷ 18
= 5 r 6
Number of Block P along the breadth of the box
= 96 ÷ 32
= 3
Number of Block P to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 24 cm; (b) 15