PSLE A rectangular block F was cut along the dotted line into two smaller rectangular blocks of equal height, G and H, as shown. The volume of H is 14336 cm
3 more than that of G.
- What is the height of each block?
- Sean packed 8 of block H such that they fit exactly into a box with a square base. The box has the same height as H. At most, how many of block G can be packed into such a box?
(a)
Base area of Block G
= 20 x 32
= 640 cm
2 Base area of Block H
= 48 x 32
= 1152 cm
2 Base area of Block H more than Block G
= 1152 - 640
= 512 cm
2 Height of each block
= 14336 ÷ 512
= 28 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block G along the length of the box
= 96 ÷ 20
= 4 r 16
Number of Block G along the breadth of the box
= 96 ÷ 32
= 3
Number of Block G to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 28 cm; (b) 12