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 22464 cm
3 more than that of C.
- What is the height of each block?
- Ahmad 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
= 22 x 32
= 704 cm
2 Base area of Block D
= 48 x 32
= 1536 cm
2 Base area of Block D more than Block C
= 1536 - 704
= 832 cm
2 Height of each block
= 22464 ÷ 832
= 27 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block C along the length of the box
= 96 ÷ 22
= 4 r 8
Number of Block C along the breadth of the box
= 96 ÷ 32
= 3
Number of Block C to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 27 cm; (b) 12