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 1664 cm
3 more than that of C.
- What is the height of each block?
- Daniel packed 8 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 16
= 160 cm
2 Base area of Block D
= 24 x 16
= 288 cm
2 Base area of Block D more than Block C
= 288 - 160
= 128 cm
2 Height of each block
= 1664 ÷ 128
= 13 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block C along the length of the box
= 48 ÷ 10
= 4 r 8
Number of Block C along the breadth of the box
= 48 ÷ 16
= 3
Number of Block C to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 13 cm; (b) 12