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 6864 cm
3 more than that of C.
- What is the height of each block?
- John 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
= 9 x 22
= 198 cm
2 Base area of Block D
= 33 x 22
= 726 cm
2 Base area of Block D more than Block C
= 726 - 198
= 528 cm
2 Height of each block
= 6864 ÷ 528
= 13 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block C along the length of the box
= 66 ÷ 9
= 7 r 3
Number of Block C along the breadth of the box
= 66 ÷ 22
= 3
Number of Block C to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 13 cm; (b) 21