2. The surface area of the cylinder is150.72cm2, and the radius of the bottom surface is 2cm. Find its volume.
A cylindrical wood is 2 meters long. After cutting it into four equal parts, the surface area increased by 18.84 cm2. What is the volume of each log after cutting?
4. Cut a round steel with a base diameter of 20 cm into two sections of the same round steel, and the sum of the surface areas of the two sections is 7536 square centimeters. How many cubic centimeters was the original round steel?
5. What is the height of a cuboid iron block with a length and width of 10 cm and a height of 3 1.4 cm after forging into a cone with a bottom radius of 10 cm?
6. A cylindrical container with a bottom diameter of 20 cm is filled with some water, and a conical plumb hammer with a height of 10 cm and a bottom radius of 12 cm is immersed in the water. How many centimeters did the water in the container drop when the plumb hammer was taken out of the water?
7. Divide the bottom surface of a cylinder into several sectors on average, then cut and spliced into several sectors, and then cut and spliced into an approximate cuboid, with the surface area increased by 200 square centimeters. As we all know, the height of a cylinder is 20 cubic centimeters. Find the volume of a cylinder.
8. After cutting a cylinder into the largest cone, the volume of the cut part is 30 cubic centimeters more than that of the cone, and the volume of the original cylinder is calculated.
9. What is the volume of a cube after it is cut into the largest cone?
10, cut a cube into the largest cylinder. If the side area of a cylinder is 3 14cm2, find the surface area of the cube.
1 1. A cuboid block with a length of 55 cm, a width of 40 cm and a height of 30 cm is processed into the largest conical block. How many cubic centimeters is the volume of a cone?
12. Cut a cylindrical piece of wood into two sections along the diameter direction. It is known that the bottom diameter of the cylinder is 10 cm and the height is 15 cm. Find the surface area of half a cylinder. 1. The surface area of a cylinder is 100 square centimeter, the volume is 200 cubic centimeters, and what is the bottom area?
Square centimeters?
2πr？ 0? 5+2πrh= 100
πr？ 0? 5h=200
Solve this system of equations and get πr? 0? A value of 5 is sufficient.
2. The surface area of the cylinder is150.72cm2, and the radius of the bottom surface is 2cm. Find its volume.
2πr？ 0? 5+2πrh= 150.72
R = 2 is substituted into the above formula to find H, and then πr? 0? Five hours is enough.
A cylindrical wood is 2 meters long. After cutting it into four parts, the surface area increased by 18.84 square meters.
Centimeter. What is the volume of each log after cutting?
πr？ 0? 5= 18.84÷6
H = 0.5 for πr? 0? Five hours is enough.
4. Cut the round steel with a bottom diameter of 20 cm into two identical round steel parts, and the sum of the surface areas of the two parts.
It's 7536 square centimeters. How many cubic centimeters was the original round steel?
r = 20 \2
4πr？ 0? 5+2πrh=7536
Find πr? 0? Five hours is enough.
5. Forging a cuboid iron block with the length and width of 10 cm, the height of 3 1.4 cm and the bottom radius of 10.
What is the height behind the cone of a one-centimeter cone?
1/3πr？ 0? 5h = 10× 10×3 1.4
Just solve h.
6. Put some water into a cylindrical container with a bottom diameter of 20 cm, and place a container with a height of 10 cm and a cylindrical bottom half.
A conical plumb hammer with a diameter of 12 cm sank into the water. When the plumb hammer is taken out of the water, the water in the container drops.
How many centimeters have you lost?
π(20÷2)? 0? 5x= 1/3× 12π？ 0? 5× 10, just solve x.
7. Divide the bottom of a cylinder into several sectors on average, and then cut and splice it into an approximate cuboid.
The surface area has increased by 200 square centimeters. Suppose the height of a cylinder is 20 cm, and find the volume of the cylinder.
2πrh=200
h=20
Solve πr? 0? Five hours is enough.
8. After the cylinder is cut into the largest cone, the volume of the cut part is 30 cubic meters more than that of the cone.
Cm, find the volume of the original cylinder.
90 cubic centimeters
9. After the cube is cut into the largest cone, the cone volume is the cube.
Which part of the product?
If the side length of a cube is 2r, then the volume of the cube is 8r^3, the volume of the cylinder is 2πr^3, and the volume of the cone is 2/3π r 3.
.
10, cut a cube into the largest cylinder. If the side area of a cylinder is 3 14 square.
Cm, find the surface area of the cube.
If the side length of a cube is 2r, then the lateral area of a cylinder is 4πr? 0? 5. Find the surface area of the R cube.
6r？ 0? 5。
1 1, a cuboid block with a length of 55 cm, a width of 40 cm and a height of 30 cm, was processed into the most
A big cone-shaped block of wood. What is the volume of this cone-shaped block of wood?
It is discussed in three situations.
1. Take 55cm as the height of the cone block: 1/3π (30 ÷ 2)? 0? 5×55;
2. Take 40cm as the height of the cone: 1/3π (30 ÷ 2)? 0? 5×40;
3. Take 30cm as the height of the conical block: 1/3π (40 ÷ 2)? 0? 5×30;
Calculation and comparison.
12. Cut a cylindrical piece of wood into two sections along the diameter direction. It is known that the diameter of the cylinder bottom is 10 cm.
M, the height is 15cm, and find the surface area of half a cylinder.
π( 10÷2)? 0? 5 × 15+ 10× 15 +5π× 15
Just remember the volume formula of cylindrical cone.