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 1530 cm
3 more than that of C.
- What is the height of each block?
- Gabriel 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
= 5 x 12
= 60 cm
2 Base area of Block D
= 18 x 12
= 162 cm
2 Base area of Block D more than Block C
= 162 - 60
= 102 cm
2 Height of each block
= 1530 ÷ 102
= 15 cm
(b)
Base area of the box
= 8 x 162
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block C along the length of the box
= 36 ÷ 5
= 7 r 1
Number of Block C along the breadth of the box
= 36 ÷ 12
= 3
Number of Block C to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 15 cm; (b) 21