PSLE A rectangular block E was cut along the dotted line into two smaller rectangular blocks of equal height, F and G, as shown. The volume of G is 4590 cm
3 more than that of F.
- What is the height of each block?
- Sean packed 6 of block G such that they fit exactly into a box with a square base. The box has the same height as G. At most, how many of block F can be packed into such a box?
(a)
Base area of Block F
= 10 x 18
= 180 cm
2 Base area of Block G
= 27 x 18
= 486 cm
2 Base area of Block G more than Block F
= 486 - 180
= 306 cm
2 Height of each block
= 4590 ÷ 306
= 15 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block F along the length of the box
= 54 ÷ 10
= 5 r 4
Number of Block F along the breadth of the box
= 54 ÷ 18
= 3
Number of Block F to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 15 cm; (b) 15