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 5376 cm
3 more than that of D.
- What is the height of each block?
- Seth packed 8 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
= 11 x 24
= 264 cm
2 Base area of Block E
= 36 x 24
= 648 cm
2 Base area of Block E more than Block D
= 648 - 264
= 384 cm
2 Height of each block
= 5376 ÷ 384
= 14 cm
(b)
Base area of the box
= 8 x 648
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block D along the length of the box
= 72 ÷ 11
= 6 r 6
Number of Block D along the breadth of the box
= 72 ÷ 24
= 3
Number of Block D to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 14 cm; (b) 18