PSLE A rectangular block J was cut along the dotted line into two smaller rectangular blocks of equal height, K and L, as shown. The volume of L is 22400 cm
3 more than that of K.
- What is the height of each block?
- Riordan packed 6 of block L such that they fit exactly into a box with a square base. The box has the same height as L. At most, how many of block K can be packed into such a box?
(a)
Base area of Block K
= 13 x 32
= 416 cm
2 Base area of Block L
= 48 x 32
= 1536 cm
2 Base area of Block L more than Block K
= 1536 - 416
= 1120 cm
2 Height of each block
= 22400 ÷ 1120
= 20 cm
(b)
Base area of the box
= 6 x 1536
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block K along the length of the box
= 96 ÷ 13
= 7 r 5
Number of Block K along the breadth of the box
= 96 ÷ 32
= 3
Number of Block K to pack into the box at most
= 7 x 3
= 21
Answer(s): (a) 20 cm; (b) 21