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 16632 cm
3 more than that of K.
- What is the height of each block?
- Nick 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
= 15 x 28
= 420 cm
2 Base area of Block L
= 42 x 28
= 1176 cm
2 Base area of Block L more than Block K
= 1176 - 420
= 756 cm
2 Height of each block
= 16632 ÷ 756
= 22 cm
(b)
Base area of the box
= 6 x 1176
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block K along the length of the box
= 84 ÷ 15
= 5 r 9
Number of Block K along the breadth of the box
= 84 ÷ 28
= 3
Number of Block K to pack into the box at most
= 5 x 3
= 15
Answer(s): (a) 22 cm; (b) 15