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 21390 cm
3 more than that of Q.
- What is the height of each block?
- Bobby 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
= 14 x 30
= 420 cm
2 Base area of Block R
= 45 x 30
= 1350 cm
2 Base area of Block R more than Block Q
= 1350 - 420
= 930 cm
2 Height of each block
= 21390 ÷ 930
= 23 cm
(b)
Base area of the box
= 6 x 1350
= 8100 cm
3 Length of the box
= √8100
= 90 cm
Number of Block Q along the length of the box
= 90 ÷ 14
= 6 r 6
Number of Block Q along the breadth of the box
= 90 ÷ 30
= 3
Number of Block Q to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 23 cm; (b) 18