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 3840 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
= 9 x 16
= 144 cm
2 Base area of Block F
= 24 x 16
= 384 cm
2 Base area of Block F more than Block E
= 384 - 144
= 240 cm
2 Height of each block
= 3840 ÷ 240
= 16 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 ÷ 9
= 5 r 3
Number of Block E along the breadth of the box
= 48 ÷ 16
= 3
Number of Block E to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 16 cm; (b) 15