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 70 cm
3 more than that of P.
- What is the height of each block?
- Ken 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
= 1 x 4
= 4 cm
2 Base area of Block Q
= 6 x 4
= 18 cm
2 Base area of Block Q more than Block P
= 18 - 4
= 14 cm
2 Height of each block
= 70 ÷ 14
= 5 cm
(b)
Base area of the box
= 8 x 18
= 144 cm
3 Length of the box
= √144
= 12 cm
Number of Block P along the length of the box
= 12 ÷ 1
= 12 r 0
Number of Block P along the breadth of the box
= 12 ÷ 4
= 3
Number of Block P to pack into the box at most
= 12 x 3
= 36
Answer(s): (a) 5 cm; (b) 36