PSLE A rectangular block M was cut along the dotted line into two smaller rectangular blocks of equal height, N and P, as shown. The volume of P is 16240 cm
3 more than that of N.
- What is the height of each block?
- Vincent packed 6 of block P such that they fit exactly into a box with a square base. The box has the same height as P. At most, how many of block N can be packed into such a box?
(a)
Base area of Block N
= 13 x 28
= 364 cm
2 Base area of Block P
= 42 x 28
= 1176 cm
2 Base area of Block P more than Block N
= 1176 - 364
= 812 cm
2 Height of each block
= 16240 ÷ 812
= 20 cm
(b)
Base area of the box
= 6 x 1176
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block N along the length of the box
= 84 ÷ 13
= 6 r 6
Number of Block N along the breadth of the box
= 84 ÷ 28
= 3
Number of Block N to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 20 cm; (b) 18