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 11232 cm
3 more than that of Q.
- What is the height of each block?
- Oscar 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
= 15 x 26
= 390 cm
2 Base area of Block R
= 39 x 26
= 1014 cm
2 Base area of Block R more than Block Q
= 1014 - 390
= 624 cm
2 Height of each block
= 11232 ÷ 624
= 18 cm
(b)
Base area of the box
= 6 x 1014
= 6084 cm
3 Length of the box
= √6084
= 78 cm
Number of Block Q along the length of the box
= 78 ÷ 15
= 5 r 3
Number of Block Q along the breadth of the box
= 78 ÷ 26
= 3
Number of Block Q to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 18 cm; (b) 15