PSLE A rectangular block L was cut along the dotted line into two smaller rectangular blocks of equal height, M and N, as shown. The volume of N is 1080 cm
3 more than that of M.
- What is the height of each block?
- John packed 6 of block N such that they fit exactly into a box with a square base. The box has the same height as N. At most, how many of block M can be packed into such a box?
(a)
Base area of Block M
= 6 x 10
= 60 cm
2 Base area of Block N
= 15 x 10
= 150 cm
2 Base area of Block N more than Block M
= 150 - 60
= 90 cm
2 Height of each block
= 1080 ÷ 90
= 12 cm
(b)
Base area of the box
= 6 x 150
= 900 cm
3 Length of the box
= √900
= 30 cm
Number of Block M along the length of the box
= 30 ÷ 6
= 5 r 0
Number of Block M along the breadth of the box
= 30 ÷ 10
= 3
Number of Block M to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 12 cm; (b) 15