PSLE A rectangular block F was cut along the dotted line into two smaller rectangular blocks of equal height, G and H, as shown. The volume of H is 6156 cm
3 more than that of G.
- What is the height of each block?
- Michael packed 6 of block H such that they fit exactly into a box with a square base. The box has the same height as H. At most, how many of block G can be packed into such a box?
(a)
Base area of Block G
= 9 x 18
= 162 cm
2 Base area of Block H
= 27 x 18
= 486 cm
2 Base area of Block H more than Block G
= 486 - 162
= 324 cm
2 Height of each block
= 6156 ÷ 324
= 19 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block G along the length of the box
= 54 ÷ 9
= 6 r 0
Number of Block G along the breadth of the box
= 54 ÷ 18
= 3
Number of Block G to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 19 cm; (b) 18