PSLE A rectangular block C was cut along the dotted line into two smaller rectangular blocks of equal height, D and E, as shown. The volume of E is 9240 cm
3 more than that of D.
- What is the height of each block?
- Asher packed 6 of block E such that they fit exactly into a box with a square base. The box has the same height as E. At most, how many of block D can be packed into such a box?
(a)
Base area of Block D
= 12 x 22
= 264 cm
2 Base area of Block E
= 33 x 22
= 726 cm
2 Base area of Block E more than Block D
= 726 - 264
= 462 cm
2 Height of each block
= 9240 ÷ 462
= 20 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block D along the length of the box
= 66 ÷ 12
= 5 r 6
Number of Block D along the breadth of the box
= 66 ÷ 22
= 3
Number of Block D to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 20 cm; (b) 15