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 2730 cm
3 more than that of E.
- What is the height of each block?
- Rael 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
= 8 x 14
= 112 cm
2 Base area of Block F
= 21 x 14
= 294 cm
2 Base area of Block F more than Block E
= 294 - 112
= 182 cm
2 Height of each block
= 2730 ÷ 182
= 15 cm
(b)
Base area of the box
= 6 x 294
= 1764 cm
3 Length of the box
= √1764
= 42 cm
Number of Block E along the length of the box
= 42 ÷ 8
= 5 r 2
Number of Block E along the breadth of the box
= 42 ÷ 14
= 3
Number of Block E to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 15 cm; (b) 15