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 1920 cm
3 more than that of Q.
- What is the height of each block?
- Caden 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
= 10 x 16
= 160 cm
2 Base area of Block R
= 24 x 16
= 288 cm
2 Base area of Block R more than Block Q
= 288 - 160
= 128 cm
2 Height of each block
= 1920 ÷ 128
= 15 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block Q along the length of the box
= 48 ÷ 10
= 4 r 8
Number of Block Q along the breadth of the box
= 48 ÷ 16
= 3
Number of Block Q to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 15 cm; (b) 12