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 1664 cm
3 more than that of P.
- What is the height of each block?
- Justin 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
= 10 x 16
= 160 cm
2 Base area of Block Q
= 24 x 16
= 288 cm
2 Base area of Block Q more than Block P
= 288 - 160
= 128 cm
2 Height of each block
= 1664 ÷ 128
= 13 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block P along the length of the box
= 48 ÷ 10
= 4 r 8
Number of Block P along the breadth of the box
= 48 ÷ 16
= 3
Number of Block P to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 13 cm; (b) 12