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 14168 cm
3 more than that of B.
- What is the height of each block?
- Howard 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
= 19 x 28
= 532 cm
2 Base area of Block C
= 42 x 28
= 1176 cm
2 Base area of Block C more than Block B
= 1176 - 532
= 644 cm
2 Height of each block
= 14168 ÷ 644
= 22 cm
(b)
Base area of the box
= 6 x 1176
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block B along the length of the box
= 84 ÷ 19
= 4 r 8
Number of Block B along the breadth of the box
= 84 ÷ 28
= 3
Number of Block B to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 22 cm; (b) 12