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 3584 cm
3 more than that of E.
- What is the height of each block?
- Eric 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 16
= 128 cm
2 Base area of Block F
= 24 x 16
= 384 cm
2 Base area of Block F more than Block E
= 384 - 128
= 256 cm
2 Height of each block
= 3584 ÷ 256
= 14 cm
(b)
Base area of the box
= 6 x 384
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block E along the length of the box
= 48 ÷ 8
= 6 r 0
Number of Block E along the breadth of the box
= 48 ÷ 16
= 3
Number of Block E to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 14 cm; (b) 18