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 8800 cm
3 more than that of Y.
- What is the height of each block?
- Paul 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
= 13 x 22
= 286 cm
2 Base area of Block Z
= 33 x 22
= 726 cm
2 Base area of Block Z more than Block Y
= 726 - 286
= 440 cm
2 Height of each block
= 8800 ÷ 440
= 20 cm
(b)
Base area of the box
= 6 x 726
= 4356 cm
3 Length of the box
= √4356
= 66 cm
Number of Block Y along the length of the box
= 66 ÷ 13
= 5 r 1
Number of Block Y along the breadth of the box
= 66 ÷ 22
= 3
Number of Block Y to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 20 cm; (b) 15