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 10944 cm
3 more than that of N.
- What is the height of each block?
- Oliver 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
= 17 x 24
= 408 cm
2 Base area of Block P
= 36 x 24
= 864 cm
2 Base area of Block P more than Block N
= 864 - 408
= 456 cm
2 Height of each block
= 10944 ÷ 456
= 24 cm
(b)
Base area of the box
= 6 x 864
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block N along the length of the box
= 72 ÷ 17
= 4 r 4
Number of Block N along the breadth of the box
= 72 ÷ 24
= 3
Number of Block N to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 24 cm; (b) 12