solve
After being cut into three parts, four bottom areas were added.
Sbase = RR π = 6× 6× 3.14 =113.04 (square decimeter)
Increased surface area = 4s = 4x113.04 = 452.16 (square decimeter).
A: The surface area has increased by 452. 16 square decimeter.
2. The worker's uncle sawed a 1 meter-high cylindrical wood into two sections along the direction parallel to the bottom. At this time, the surface area increased by 25. 12 square decimeter. What is the bottom radius of this material?
solve
The increased surface area is 2 bottom areas,
The area of the bottom of the cylinder =25. 12÷2= 12.56 (square decimeter)
According to S=rrπ.
RR = S/π= 12.56÷3. 14 = 4
R=2 (decimeter)
The bottom radius of this material is 2 decimeters.
3. The bottom of the cylinder is 4m in diameter and 6m in height. Cut the cylinder in half along the diameter of the bottom surface and find out how much the surface area of the cylinder has increased.
solve
Add two or two rectangles with diameter and height.
Rectangular area =4×6=24 (square decimeter)
Increased surface area = rectangular area ×2=24×2=48 (square decimeter)
A: The surface area of this cylinder has increased by 48 square decimeters.
4. Cut a square block with a length of 10 cm into the largest cylinder. What is the surface area of this cylinder?
The height and base diameter of the cylinder are equal to the cube side length of 10 cm.
Lateral area of cylinder = height× circumference =10×10× 3.14 = 314 (square centimeter).
Cylinder bottom area = (10 ÷ 2) × (10 ÷ 2 )× 3.14 = 78.5 (square centimeter).
Surface area of cylinder = lateral area+bottom area× 2 = 314+78.5× 2 = 471(square centimeter).
A: The surface area of this cylinder is 47 1 cm2.
5. The surface area of the cylinder is1884cm2, and the radius of the bottom surface is10cm. What is its height?
solve
First, calculate the bottom area, subtract two bottom areas from the surface area, and the remaining area is the lateral area, thus calculating the height of the cylinder.
Bottom area =10×10× 3.14 = 314 (square centimeter)
Bottom circumference = (10+10) × 3.14 = 62.8 (cm)
Lateral area of cylinder = surface area-bottom area× 2 =1884-314× 2 =1256 (square centimeter).
Cylinder height = side area ÷ perimeter = 1256÷62.8=20 (cm).
A: Its height is 20 cm.