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 2548 cm
3 more than that of Q.
- What is the height of each block?
- Owen 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
= 7 x 14
= 98 cm
2 Base area of Block R
= 21 x 14
= 294 cm
2 Base area of Block R more than Block Q
= 294 - 98
= 196 cm
2 Height of each block
= 2548 ÷ 196
= 13 cm
(b)
Base area of the box
= 6 x 294
= 1764 cm
3 Length of the box
= √1764
= 42 cm
Number of Block Q along the length of the box
= 42 ÷ 7
= 6 r 0
Number of Block Q along the breadth of the box
= 42 ÷ 14
= 3
Number of Block Q to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 13 cm; (b) 18