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 2160 cm
3 more than that of M.
- What is the height of each block?
- Harry packed 8 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
= 9 x 16
= 144 cm
2 Base area of Block N
= 24 x 16
= 288 cm
2 Base area of Block N more than Block M
= 288 - 144
= 144 cm
2 Height of each block
= 2160 ÷ 144
= 15 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block M along the length of the box
= 48 ÷ 9
= 5 r 3
Number of Block M along the breadth of the box
= 48 ÷ 16
= 3
Number of Block M to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 15 cm; (b) 15