PSLE A rectangular block P was cut along the dotted line into two smaller rectangular blocks of equal height, Q and R, as shown. The volume of R is 420 cm
3 more than that of Q.
- What is the height of each block?
- Sam packed 6 of block R such that they fit exactly into a box with a square base. The box has the same height as R. At most, how many of block Q can be packed into such a box?
(a)
Base area of Block Q
= 2 x 6
= 12 cm
2 Base area of Block R
= 9 x 6
= 54 cm
2 Base area of Block R more than Block Q
= 54 - 12
= 42 cm
2 Height of each block
= 420 ÷ 42
= 10 cm
(b)
Base area of the box
= 6 x 54
= 324 cm
3 Length of the box
= √324
= 18 cm
Number of Block Q along the length of the box
= 18 ÷ 2
= 9 r 0
Number of Block Q along the breadth of the box
= 18 ÷ 6
= 3
Number of Block Q to pack into the box at most
= 9 x 3
= 27
Answer(s): (a) 10 cm; (b) 27