PSLE A rectangular block B was cut along the dotted line into two smaller rectangular blocks of equal height, C and D, as shown. The volume of D is 2912 cm
3 more than that of C.
- What is the height of each block?
- Daniel packed 6 of block D such that they fit exactly into a box with a square base. The box has the same height as D. At most, how many of block C can be packed into such a box?
(a)
Base area of Block C
= 8 x 14
= 112 cm
2 Base area of Block D
= 21 x 14
= 294 cm
2 Base area of Block D more than Block C
= 294 - 112
= 182 cm
2 Height of each block
= 2912 ÷ 182
= 16 cm
(b)
Base area of the box
= 6 x 294
= 1764 cm
3 Length of the box
= √1764
= 42 cm
Number of Block C along the length of the box
= 42 ÷ 8
= 5 r 2
Number of Block C along the breadth of the box
= 42 ÷ 14
= 3
Number of Block C to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 16 cm; (b) 15