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 154 cm
3 more than that of C.
- What is the height of each block?
- Carl 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
= 1 x 4
= 4 cm
2 Base area of Block D
= 6 x 4
= 18 cm
2 Base area of Block D more than Block C
= 18 - 4
= 14 cm
2 Height of each block
= 154 ÷ 14
= 11 cm
(b)
Base area of the box
= 8 x 18
= 144 cm
3 Length of the box
= √144
= 12 cm
Number of Block C along the length of the box
= 12 ÷ 1
= 12 r 0
Number of Block C along the breadth of the box
= 12 ÷ 4
= 3
Number of Block C to pack into the box at most
= 12 x 3
= 36
Answer(s): (a) 11 cm; (b) 36