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 12000 cm
3 more than that of E.
- What is the height of each block?
- Luis 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
= 11 x 24
= 264 cm
2 Base area of Block F
= 36 x 24
= 864 cm
2 Base area of Block F more than Block E
= 864 - 264
= 600 cm
2 Height of each block
= 12000 ÷ 600
= 20 cm
(b)
Base area of the box
= 6 x 864
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block E along the length of the box
= 72 ÷ 11
= 6 r 6
Number of Block E along the breadth of the box
= 72 ÷ 24
= 3
Number of Block E to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 20 cm; (b) 18