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 5200 cm
3 more than that of Q.
- What is the height of each block?
- Simon 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
= 10 x 20
= 200 cm
2 Base area of Block R
= 30 x 20
= 600 cm
2 Base area of Block R more than Block Q
= 600 - 200
= 400 cm
2 Height of each block
= 5200 ÷ 400
= 13 cm
(b)
Base area of the box
= 6 x 600
= 3600 cm
3 Length of the box
= √3600
= 60 cm
Number of Block Q along the length of the box
= 60 ÷ 10
= 6 r 0
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) 13 cm; (b) 18