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 13832 cm
3 more than that of S.
- What is the height of each block?
- John 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
= 16 x 28
= 448 cm
2 Base area of Block T
= 42 x 28
= 1176 cm
2 Base area of Block T more than Block S
= 1176 - 448
= 728 cm
2 Height of each block
= 13832 ÷ 728
= 19 cm
(b)
Base area of the box
= 6 x 1176
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block S along the length of the box
= 84 ÷ 16
= 5 r 4
Number of Block S along the breadth of the box
= 84 ÷ 28
= 3
Number of Block S to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 19 cm; (b) 15