!problems on areas and volumes

1. A wooden box with length 20cm,width 15cm and height 5 cm is saw intoa cuboid. Find the side of the cube.

When a rectangular wooden box is saw (鋸) into the cuboid, the sideof the cube can only be the shortest side of the wooden box.
Hence, the side of the cube = 5 cm


2. A rectangular lawn 100m and 50m wide issurrounded by a path of 4m wide. Find the area of the path.

Total area of the lawn and the path
= (100 + 4) x (50 + 4) m²
= 104 x 54 m²
= 5616 m²

Area of the lawn
= 100 x 50 m²
= 5000 m²

Area of the path
= 5616 - 5000 m²
= 616 m²


3. A cubic room of volume 500m is to fill with cuboid box of side 5m.Find thenumber of boxes that can be put in.

Number of boxes can be put in
= (500/5)³
= 1 000 000


4. A rectangular floor 4.8m by 3.2m is to be tiledwith square tiles measuring 0.4m by 0.4m.How many tiles will be used?

Number of tiles used
= (4.8/0.4) x (3.2/0.4)
= 12 x 8
= 96


5. What is the greatest number of bricks each 2cmby 2cm by 2cm which can be packed into a box 11 cm by 12cm by 4m?

Greatest number of bricks that can be line up on the side 11 cm
= integer part of (11/2)
= 5

Greatest number of bricks that can be line up on the side 12 cm
= integer part of (12/2)
= 6

Greatest number of bricks that can be line up on the side 4 cm
= integer part of (4/2)
= 2

Greatest number of bricks that can be packed
= 5 x 6 x 2
= 60

2013-02-16 23:07:04 補充：
6.
Minimum volume of the box
= (42)² x 25 cm³
= 44 100 cm³ ...... (answer)

2013-02-16 23:07:20 補充：
6.
Minimum volume of the box
= (42)² x 25 cm³
= 44 100 cm³ ...... (answer)

2013-02-16 23:09:27 補充：
「補充」的意思是補充原題目的遺漏，或者提供原題目的補充資料，而不是用來不斷附加題目。

2013-02-16 23:09:45 補充：
「補充」的意思是補充原題目的遺漏，或者提供原題目的補充資料，而不是用來不斷附加題目。