PSLE A rectangular block B was cut along the dotted line into two smaller rectangular blocks of equal height, C and D, as shown. The volume of D is 10360 cm
3 more than that of C.
- What is the height of each block?
- Julian packed 8 of block D such that they fit exactly into a box with a square base. The box has the same height as D. At most, how many of block C can be packed into such a box?
(a)
Base area of Block C
= 13 x 28
= 364 cm
2 Base area of Block D
= 42 x 28
= 882 cm
2 Base area of Block D more than Block C
= 882 - 364
= 518 cm
2 Height of each block
= 10360 ÷ 518
= 20 cm
(b)
Base area of the box
= 8 x 882
= 7056 cm
3 Length of the box
= √7056
= 84 cm
Number of Block C along the length of the box
= 84 ÷ 13
= 6 r 6
Number of Block C along the breadth of the box
= 84 ÷ 28
= 3
Number of Block C to pack into the box at most
= 6 x 3
= 18
Answer(s): (a) 20 cm; (b) 18