PSLE A rectangular block N was cut along the dotted line into two smaller rectangular blocks of equal height, P and Q, as shown. The volume of Q is 8316 cm
3 more than that of P.
- What is the height of each block?
- Fred packed 8 of block Q such that they fit exactly into a box with a square base. The box has the same height as Q. At most, how many of block P can be packed into such a box?
(a)
Base area of Block P
= 15 x 28
= 420 cm
2 Base area of Block Q
= 42 x 28
= 882 cm
2 Base area of Block Q more than Block P
= 882 - 420
= 462 cm
2 Height of each block
= 8316 ÷ 462
= 18 cm
(b)
Base area of the box
= 8 x 882
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block P along the length of the box
= 84 ÷ 15
= 5 r 9
Number of Block P along the breadth of the box
= 84 ÷ 28
= 3
Number of Block P to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 18 cm; (b) 15