PSLE A rectangular block A was cut along the dotted line into two smaller rectangular blocks of equal height, B and C, as shown. The volume of C is 768 cm
3 more than that of B.
- What is the height of each block?
- Ivan packed 6 of block C such that they fit exactly into a box with a square base. The box has the same height as C. At most, how many of block B can be packed into such a box?
(a)
Base area of Block B
= 4 x 8
= 32 cm
2 Base area of Block C
= 12 x 8
= 96 cm
2 Base area of Block C more than Block B
= 96 - 32
= 64 cm
2 Height of each block
= 768 ÷ 64
= 12 cm
(b)
Base area of the box
= 6 x 96
= 576 cm
3 Length of the box
= √576
= 24 cm
Number of Block B along the length of the box
= 24 ÷ 4
= 6 r 0
Number of Block B along the breadth of the box
= 24 ÷ 8
= 3
Number of Block B to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 12 cm; (b) 18