PSLE A rectangular block X was cut along the dotted line into two smaller rectangular blocks of equal height, Y and Z, as shown. The volume of Z is 2040 cm
3 more than that of Y.
- What is the height of each block?
- Archie packed 6 of block Z such that they fit exactly into a box with a square base. The box has the same height as Z. At most, how many of block Y can be packed into such a box?
(a)
Base area of Block Y
= 8 x 12
= 96 cm
2 Base area of Block Z
= 18 x 12
= 216 cm
2 Base area of Block Z more than Block Y
= 216 - 96
= 120 cm
2 Height of each block
= 2040 ÷ 120
= 17 cm
(b)
Base area of the box
= 6 x 216
= 1296 cm
3 Length of the box
= √1296
= 36 cm
Number of Block Y along the length of the box
= 36 ÷ 8
= 4 r 4
Number of Block Y along the breadth of the box
= 36 ÷ 12
= 3
Number of Block Y to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 17 cm; (b) 12