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 4896 cm
3 more than that of C.
- What is the height of each block?
- Lee 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
= 10 x 18
= 180 cm
2 Base area of Block D
= 27 x 18
= 486 cm
2 Base area of Block D more than Block C
= 486 - 180
= 306 cm
2 Height of each block
= 4896 ÷ 306
= 16 cm
(b)
Base area of the box
= 6 x 486
= 2916 cm
3 Length of the box
= √2916
= 54 cm
Number of Block C along the length of the box
= 54 ÷ 10
= 5 r 4
Number of Block C along the breadth of the box
= 54 ÷ 18
= 3
Number of Block C to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 16 cm; (b) 15