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 3808 cm
3 more than that of S.
- What is the height of each block?
- Reggie packed 6 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
= 7 x 16
= 112 cm
2 Base area of Block T
= 24 x 16
= 384 cm
2 Base area of Block T more than Block S
= 384 - 112
= 272 cm
2 Height of each block
= 3808 ÷ 272
= 14 cm
(b)
Base area of the box
= 6 x 384
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block S along the length of the box
= 48 ÷ 7
= 6 r 6
Number of Block S along the breadth of the box
= 48 ÷ 16
= 3
Number of Block S to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 14 cm; (b) 18