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 4608 cm
3 more than that of P.
- What is the height of each block?
- Howard 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
= 11 x 18
= 198 cm
2 Base area of Block Q
= 27 x 18
= 486 cm
2 Base area of Block Q more than Block P
= 486 - 198
= 288 cm
2 Height of each block
= 4608 ÷ 288
= 16 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block P along the length of the box
= 54 ÷ 11
= 4 r 10
Number of Block P along the breadth of the box
= 54 ÷ 18
= 3
Number of Block P to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 16 cm; (b) 12