The two right-angle sides of a right angle are 6CM and 8CM respectively. What figure can be obtained by rotating the right-angle side of 6CM as the axis? What is its volume?

Solution: You can get a cone with a radius of 8 cm at the bottom and a height of 6 cm.

Volume =1/3× 3.14× 8× 6 = 401.92 cubic centimeter.

2: The base and height of the cone and cylinder are equal.

(1) The volume of the cylinder is larger than that of the cone 18.84 cubic meters. What is the volume of a cylinder?

A cylinder with equal base and equal height is three times the volume of a cone, and the cone is regarded as a multiple of 1.

Then the volume of the cone =18.84/(3-1) = 9.42 cubic meters.

The volume of the cylinder =9.42×3=28.26 cubic meters.

(2) The sum of cylinder volume and cone volume is 18.84 cubic meters. What is the volume of this cone?

The volume of the cone =18.84/(3+1) = 4.71m3.

3. A part with a conical top and a cylindrical bottom. Their ground radius is 3 cm and their height is 5 cm. What is the volume of this part in cubic centimeters?

The volume of a cone with equal base and equal height is 1/3 of the volume of a cylinder.

Then the bottom area of the cone =3. 14×3×3=28.26 square centimeters.

The volume of the cone =1/3× 28.26× 5 = 47.1cubic centimeter.

The volume of this part = 47.1× (3+1) =188.4 cubic centimeters.

4. A pair of wheat piles are conical, the bottom circumference is 18.84M, and the height is1.8m. Put these wheat into a cylindrical granary with a bottom radius of 3CM and just fill it up. How high is this granary?

Solution: Radius of cone bottom =18.84/(2× 3.14) = 3m.

The bottom area of the cone =3. 14×3×3=28.26 square meters.

The volume of wheat =1/3× 28.26×1.8 =16.956 cubic meters.

The bottom area of the cylinder =3. 14×3×3=28.26 square meters.

Height of cylinder =16.956/28.26 = 0.6m.

5. A conical metal with a bottom radius of 6CM is completely immersed in a cylindrical container with a bottom radius of 15CM, and the water level is 0.6CM higher than the original one (water does not flow out). What is the height of this cylindrical metal?

Solution: The bottom area of the cylinder = 3.14×15×15 = 706.5 cm2.

The volume of conical metal =706.5×0.6=423.9 cubic centimeters.

The base area of the cone is 3.14× 6× 6 =113.04cm2..

Height of conical metal = 423.9× 3/113.04 =11.25cm.