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 4050 cm
3 more than that of Q.
- What is the height of each block?
- Cole 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
= 9 x 20
= 180 cm
2 Base area of Block R
= 30 x 20
= 450 cm
2 Base area of Block R more than Block Q
= 450 - 180
= 270 cm
2 Height of each block
= 4050 ÷ 270
= 15 cm
(b)
Base area of the box
= 8 x 450
= 3600 cm
3 Length of the box
= √3600
= 60 cm
Number of Block Q along the length of the box
= 60 ÷ 9
= 6 r 6
Number of Block Q along the breadth of the box
= 60 ÷ 20
= 3
Number of Block Q to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 15 cm; (b) 18