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 6720 cm
3 more than that of K.
- What is the height of each block?
- Luis packed 8 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 24
= 312 cm
2 Base area of Block L
= 36 x 24
= 648 cm
2 Base area of Block L more than Block K
= 648 - 312
= 336 cm
2 Height of each block
= 6720 ÷ 336
= 20 cm
(b)
Base area of the box
= 8 x 648
= 5184 cm
3 Length of the box
= √5184
= 72 cm
Number of Block K along the length of the box
= 72 ÷ 13
= 5 r 7
Number of Block K along the breadth of the box
= 72 ÷ 24
= 3
Number of Block K to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 20 cm; (b) 15