PSLE A rectangular block R was cut along the dotted line into two smaller rectangular blocks of equal height, S and T, as shown. The volume of T is 14400 cm
3 more than that of S.
- What is the height of each block?
- Elijah packed 8 of block T such that they fit exactly into a box with a square base. The box has the same height as T. At most, how many of block S can be packed into such a box?
(a)
Base area of Block S
= 21 x 32
= 672 cm
2 Base area of Block T
= 48 x 32
= 1152 cm
2 Base area of Block T more than Block S
= 1152 - 672
= 480 cm
2 Height of each block
= 14400 ÷ 480
= 30 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block S along the length of the box
= 96 ÷ 21
= 4 r 12
Number of Block S along the breadth of the box
= 96 ÷ 32
= 3
Number of Block S to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 30 cm; (b) 12