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 7728 cm
3 more than that of F.
- What is the height of each block?
- Cody packed 8 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
= 20 x 28
= 560 cm
2 Base area of Block G
= 42 x 28
= 882 cm
2 Base area of Block G more than Block F
= 882 - 560
= 322 cm
2 Height of each block
= 7728 ÷ 322
= 24 cm
(b)
Base area of the box
= 8 x 882
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block F along the length of the box
= 84 ÷ 20
= 4 r 4
Number of Block F along the breadth of the box
= 84 ÷ 28
= 3
Number of Block F to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 24 cm; (b) 12