PSLE A rectangular block D was cut along the dotted line into two smaller rectangular blocks of equal height, E and F, as shown. The volume of F is 6460 cm
3 more than that of E.
- What is the height of each block?
- Japheth packed 6 of block F such that they fit exactly into a box with a square base. The box has the same height as F. At most, how many of block E can be packed into such a box?
(a)
Base area of Block E
= 13 x 20
= 260 cm
2 Base area of Block F
= 30 x 20
= 600 cm
2 Base area of Block F more than Block E
= 600 - 260
= 340 cm
2 Height of each block
= 6460 ÷ 340
= 19 cm
(b)
Base area of the box
= 6 x 600
= 3600 cm
3 Length of the box
= √3600
= 60 cm
Number of Block E along the length of the box
= 60 ÷ 13
= 4 r 8
Number of Block E along the breadth of the box
= 60 ÷ 20
= 3
Number of Block E to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 19 cm; (b) 12