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 25024 cm
3 more than that of Y.
- What is the height of each block?
- Andy 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
= 14 x 32
= 448 cm
2 Base area of Block Z
= 48 x 32
= 1536 cm
2 Base area of Block Z more than Block Y
= 1536 - 448
= 1088 cm
2 Height of each block
= 25024 ÷ 1088
= 23 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block Y along the length of the box
= 96 ÷ 14
= 6 r 12
Number of Block Y along the breadth of the box
= 96 ÷ 32
= 3
Number of Block Y to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 23 cm; (b) 18