Cylinders and cones have the same bottom and height. If the volume of the cone is 30 cubic decimeters, then the volume of the cylinder is (90) cubic decimeters; If the volume of a cylinder is 30 cubic decimeters, then the volume of a cone is (10) cubic decimeters; If the sum of their volumes is 24 cubic decimeters, then the volume of the cone is (6) cubic decimeters and the volume of the cylinder is (18) cubic decimeters.

Calculate the surface area and volume of the cylinder below. Calculate the volume of the cone below. (Unit: cm)

Where are the photos?

The bottom radius of the cylindrical section of tin smoke is 2 decimeters and the height is 8 decimeters. How many square decimetres of tin does it take to make a chimney with a cross section of 10?

Solution: 2π×2×8× 10= 1004.8 (square decimeter)

A cylindrical iron bucket without a cover is 30 cm high and the bottom radius is 10 cm. How many square decimeters of iron does it take to make this bucket? If you use one method, you will get an integer. )

Solution: π×10×10+2 π×10× 30 = 2198 (square centimeter) =22 (square decimeter).

Rotate around a shorter right angle of a right triangle and find its volume.

Turn it at a longer right angle?

Can you rotate around the longest side?

Solution: Let the short right angle side of a right triangle be A and the long right angle side be B.

The volume of a circle around its shorter right angle side is π×b×b×a÷3.

The volume of a circle around its longer right angle side is π×a×a×b÷3.

Can rotate around the longest side.

Mom's teacup is put on the table like this (as shown on the right, the bottom diameter is 8 cm and the height is 15 cm).

(1) How many square centimeters does this teacup occupy on the desktop?

(2) I was afraid that my mother would be hot, so I specially put on this decorative belt. It is 5 cm wide. How many square centimeters is it? (Ignored at joints)

(3) What is the volume of this teacup?

Where are the photos?

I might as well make the teacup a cylinder.

( 1)π×4×4=50。 24 (square centimeter)

2π×4×5= 125.6 (square centimeter)

(3)π×4×4× 15=753.6 (cubic centimeter)

The volume of the cylindrical barrel is 72 cubic decimeter, and the area of the bottom of the barrel is 12 square decimeter. There is a bucket of water in it. How high is the water?

Solution: 72÷ 12=6 (decimeter)

The volume of the conical container is 300 cubic centimeters, and the height from the inside is 12 centimeters. What is its bottom area?

Solution: 300×3÷ 12=75 (square centimeter)

The diameter of the bottom surface of the semi-cylinder is 6 cm and the height is 10 cm. Find its volume.

Solution: π× 3× 3×10 ÷ 2 =141.3.