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 14848 cm
3 more than that of Y.
- What is the height of each block?
- Glen packed 8 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
= 20 x 32
= 640 cm
2 Base area of Block Z
= 48 x 32
= 1152 cm
2 Base area of Block Z more than Block Y
= 1152 - 640
= 512 cm
2 Height of each block
= 14848 ÷ 512
= 29 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block Y along the length of the box
= 96 ÷ 20
= 4 r 16
Number of Block Y along the breadth of the box
= 96 ÷ 32
= 3
Number of Block Y to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 29 cm; (b) 12