(2) A cylindrical container with a bottom radius of 10 cm holds water. Now put a conical iron block into a container and immerse it in water. Water level rise 1 cm. What is the volume of this conical iron block?
(3) Xiao Qiang made a cylindrical container with a base diameter of 10 cm and a height of 50 cm, and Xiaoming made a conical container with a base diameter of 10 cm and a height of 10 cm. Xiao Ming said to Xiao Qiang, "Fill my container with water and pour it into yours. It takes 15 times to fill it. " Is Xiao Ming right? Why?
(4) In a cylindrical bottle with a bottom radius of 10 cm and a water depth of 8 cm, an iron block with a length and width of 8 cm and a height of 15 cm should be placed. How many centimeters will the water surface rise if the iron block is put into the water vertically?
1:
5× 2× 2 = 20 (square centimeter)
2:
3.14× 5 2 = 78.5 (square centimeter)
3:
3. 14× 5× 2 = 3 1.4 (square centimeter)
The surface area of each block is:
20+78.5+31.4 =129.9 (square centimeter)
What is the volume of?
The volume of the cone is equal to the volume of the rising water, and the volume of the cone is:
3.14×102×1= 314 (cubic centimeter)
Xiao Qiang's cylindrical volume is:
3.14× (10 ÷ 2) 2× 50 = 3925 (cubic centimeter)
Xiao Ming's cone volume is:
1/3× 3.14× (10 ÷ 2) 2×10 = 785/3 (cubic centimeter)
A cylinder is a cone, and its volume is:
3925÷785/3= 15
Your topic is "Xiao Ming tells Xiao Qiang". If your topic is right, Xiao Ming is wrong. This cone is only115 of a cylinder.
If the topic is "Xiao Qiang said to Xiao Ming", Xiao Qiang is right. A cylinder is 15 times that of a cone.
An iron block with a height of 15 cm and a water depth of 8 cm, when the iron block is placed vertically, the volume of water with a height of 8 cm is:
8× 8× 8 = 5 12 (cubic centimeter)
At this time, the bottom area of water in the cylinder is the bottom area of the cylinder minus the bottom area of iron, and the bottom area of water is:
3. 14× 10 2-8× 8 = 250 (square centimeter)
So when iron comes out vertically, the height of water level rise is:
5 12 ÷ 250 = 2.048 cm