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 192 cm
3 more than that of Q.
- What is the height of each block?
- Henry 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 4
= 8 cm
2 Base area of Block R
= 6 x 4
= 24 cm
2 Base area of Block R more than Block Q
= 24 - 8
= 16 cm
2 Height of each block
= 192 ÷ 16
= 12 cm
(b)
Base area of the box
= 6 x 24
= 144 cm
3 Length of the box
= √144
= 12 cm
Number of Block Q along the length of the box
= 12 ÷ 2
= 6 r 0
Number of Block Q along the breadth of the box
= 12 ÷ 4
= 3
Number of Block Q to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 12 cm; (b) 18