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 14784 cm
3 more than that of L.
- What is the height of each block?
- Oliver packed 8 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
= 14 x 32
= 448 cm
2 Base area of Block M
= 48 x 32
= 1152 cm
2 Base area of Block M more than Block L
= 1152 - 448
= 704 cm
2 Height of each block
= 14784 ÷ 704
= 21 cm
(b)
Base area of the box
= 8 x 1152
= 9216 cm
3 Length of the box
= √9216
= 96 cm
Number of Block L along the length of the box
= 96 ÷ 14
= 6 r 12
Number of Block L along the breadth of the box
= 96 ÷ 32
= 3
Number of Block L to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 21 cm; (b) 18