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 6120 cm
3 more than that of N.
- What is the height of each block?
- Bobby packed 8 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
= 12 x 24
= 288 cm
2 Base area of Block P
= 36 x 24
= 648 cm
2 Base area of Block P more than Block N
= 648 - 288
= 360 cm
2 Height of each block
= 6120 ÷ 360
= 17 cm
(b)
Base area of the box
= 8 x 648
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block N along the length of the box
= 72 ÷ 12
= 6 r 0
Number of Block N along the breadth of the box
= 72 ÷ 24
= 3
Number of Block N to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 17 cm; (b) 18