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 11232 cm
3 more than that of C.
- What is the height of each block?
- Fred 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 24
= 240 cm
2 Base area of Block D
= 36 x 24
= 864 cm
2 Base area of Block D more than Block C
= 864 - 240
= 624 cm
2 Height of each block
= 11232 ÷ 624
= 18 cm
(b)
Base area of the box
= 6 x 864
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block C along the length of the box
= 72 ÷ 10
= 7 r 2
Number of Block C along the breadth of the box
= 72 ÷ 24
= 3
Number of Block C to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 18 cm; (b) 21