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 8096 cm
3 more than that of E.
- What is the height of each block?
- Julian 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
= 10 x 22
= 220 cm
2 Base area of Block F
= 33 x 22
= 726 cm
2 Base area of Block F more than Block E
= 726 - 220
= 506 cm
2 Height of each block
= 8096 ÷ 506
= 16 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block E along the length of the box
= 66 ÷ 10
= 6 r 6
Number of Block E along the breadth of the box
= 66 ÷ 22
= 3
Number of Block E to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 16 cm; (b) 18