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 216 cm
3 more than that of Y.
- What is the height of each block?
- Vaidev 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
= 3 x 6
= 18 cm
2 Base area of Block Z
= 9 x 6
= 54 cm
2 Base area of Block Z more than Block Y
= 54 - 18
= 36 cm
2 Height of each block
= 216 ÷ 36
= 6 cm
(b)
Base area of the box
= 6 x 54
= 324 cm
3 Length of the box
= √324
= 18 cm
Number of Block Y along the length of the box
= 18 ÷ 3
= 6 r 0
Number of Block Y along the breadth of the box
= 18 ÷ 6
= 3
Number of Block Y to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 6 cm; (b) 18