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 17500 cm
3 more than that of Y.
- What is the height of each block?
- Tommy 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
= 17 x 28
= 476 cm
2 Base area of Block Z
= 42 x 28
= 1176 cm
2 Base area of Block Z more than Block Y
= 1176 - 476
= 700 cm
2 Height of each block
= 17500 ÷ 700
= 25 cm
(b)
Base area of the box
= 6 x 1176
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block Y along the length of the box
= 84 ÷ 17
= 4 r 16
Number of Block Y along the breadth of the box
= 84 ÷ 28
= 3
Number of Block Y to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 25 cm; (b) 12