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 384 cm
3 more than that of Q.
- What is the height of each block?
- Andy packed 8 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
= 3 x 8
= 24 cm
2 Base area of Block R
= 12 x 8
= 72 cm
2 Base area of Block R more than Block Q
= 72 - 24
= 48 cm
2 Height of each block
= 384 ÷ 48
= 8 cm
(b)
Base area of the box
= 8 x 72
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block Q along the length of the box
= 24 ÷ 3
= 8 r 0
Number of Block Q along the breadth of the box
= 24 ÷ 8
= 3
Number of Block Q to pack into the box at most
= 8 x 3
= 24
Answer(s): (a) 8 cm; (b) 24