1. In a cylindrical barrel, put a section of round steel with a cross-sectional radius of 5cm. If you put it all into the water, the water level in the bucket will rise by 9 cm. If you expose the round steel to water for 8 cm, the water level in the bucket will drop by 4 cm. What is the volume of this round steel?

From "the round steel in the water is 8 cm higher than the water surface, then the water in the bucket will drop by 4 cm", we can know that:

Every 2 cm above the water level, the water in the bucket drops 1 cm.

That is to say, for every increase in water 1 cm, round steel is 2 cm less.

So "put it all in water, and the water in the bucket will rise by 9 cm",

Then the round steel is 18 cm long.

Therefore, the volume of round steel is 5× 5× 3.14×18 =1413 (cubic centimeter).

2. Divide the bottom of a cylinder into several sectors on average, and then cut it into an approximate cuboid with equal bottom and equal height. The surface area is increased by 400 square centimeters, and the height of the cylinder is known to be 20 centimeters. Find the volume of a cylinder.

The surface area of a cuboid is increased by two: a rectangle with a bottom radius * a height;

Area of rectangle: 400/2=200.

So the bottom radius is: 200/20= 10 cm.

So the volume is 3. 14 *10 *10 * 20 = 6280 cubic centimeters.