PSLE A rectangular block K was cut along the dotted line into two smaller rectangular blocks of equal height, L and M, as shown. The volume of M is 3584 cm
3 more than that of L.
- What is the height of each block?
- Carl packed 6 of block M such that they fit exactly into a box with a square base. The box has the same height as M. At most, how many of block L can be packed into such a box?
(a)
Base area of Block L
= 10 x 16
= 160 cm
2 Base area of Block M
= 24 x 16
= 384 cm
2 Base area of Block M more than Block L
= 384 - 160
= 224 cm
2 Height of each block
= 3584 ÷ 224
= 16 cm
(b)
Base area of the box
= 6 x 384
= 2304 cm
3 Length of the box
= √2304
= 48 cm
Number of Block L along the length of the box
= 48 ÷ 10
= 4 r 8
Number of Block L along the breadth of the box
= 48 ÷ 16
= 3
Number of Block L to pack into the box at most
= 4 x 3
= 12
Answer(s): (a) 16 cm; (b) 12