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 2432 cm
3 more than that of S.
- What is the height of each block?
- Oliver 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
= 10 x 16
= 160 cm
2 Base area of Block T
= 24 x 16
= 288 cm
2 Base area of Block T more than Block S
= 288 - 160
= 128 cm
2 Height of each block
= 2432 ÷ 128
= 19 cm
(b)
Base area of the box
= 8 x 288
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block S along the length of the box
= 48 ÷ 10
= 4 r 8
Number of Block S along the breadth of the box
= 48 ÷ 16
= 3
Number of Block S to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 19 cm; (b) 12