1. Given three views of a cone, as shown in the figure, the transverse area of the cone is ().

A. 12? cm2 B. 15？ Cm 2 C. 24? Cm 2 and 30 cm in diameter. Square centimeter

Test Center: Calculation of Cone

Special topic: calculation problems.

Analysis: There are only cones, cylinders and spheres in the top view. According to the fact that the front view and the left view are triangles, we can get that this geometry is a cone, so lateral area = the perimeter of the bottom? Bus length? 2.

Solution: Solution: ∵ The bottom radius is 3 and the height is 4.

? The length of that taper bushing is 5,

? Transverse area =2? rR？ 2= 15? Square centimeters.

So choose B.

Comments: Determining the diameter and height of the cone bottom from the data in the three views is the key to solve this problem; This topic embodies the mathematical thought of combining numbers with shapes. Note that the height of the cone, the length of the generatrix and the radius of the bottom form a right triangle.

2. As shown in the figure, it is known that the central angle of the sector is 60? , the radius is, and the area of the bow in the figure is ()

A.12m

Test center: calculate the sector area.

Analysis: A as AD? CB: First, calculate the height AD length on BC, then calculate the area and sector area of triangle ABC, and then subtract the area of triangle from the sector area to get the arch area.

Answer: Solution: Do you pass A as AD? CB，

∵? CAB=60？ ，AC=AB，

? △ABC is an equilateral triangle,

AC =，

? AD=AC？ sin60？ = ? =,

? △ABC area: =,

∫ Sector area: =,

? The area of the bow is =,

So choose: C.

Comments: This question mainly examines the calculation of sector area, and the key is to master the formula of sector area: S=.

3. The radius of the bottom surface of the cone is 6cm, and its side development diagram is semicircular, so the length of the generatrix of the cone is ().

A.9 cm wide 12 cm long 15 cm long 18 cm long.

Solution: Solution: The length of the generatrix of the cone =2? 6? = 12cm，

So choose B.

Comments: This question examines the solution of the length of the cone bus, paying attention to the knowledge point that the arc length of the cone is equal to the circumference of the bottom surface.

4. As shown in the figure, in the rectangular ABCD, AB=5 and AD= 12. If the rectangular ABCD rotates twice on the straight line L as shown in the figure, the length of the path that point B passes during the two rotations is ().

A.B. 13？ C. 25？ Cao 25

Analysis: connect BD, B? D, first calculate the length of BD according to Pythagorean theorem, then calculate the length of, according to the arc length formula, and then sum up and calculate the length of the path that point B passes through during the two rotations.

Solution: connect BD, B? d，AB = 5，AD= 12，？ BD= = 13，

? = = ,∵ = =6? ,

? The path length of point B after two revolutions is: +6? =, so choose: a.

Comments: This topic mainly examines the calculation of arc length and the application of Pythagorean theorem. The key is to master the formula l=.

5. As shown in the figure, in △ABC,? ACB=90？ ,? ABC=30？ ，AB=2。 Turn △ABC 60 counterclockwise around the right-angled vertex C? Get △A？ b？ c？ , the length of the path turned by point B is ()

A. BC?

Test center: the nature of rotation; Calculation of arc length.

Analysis: Is the length of BC obtained by using the relationship of acute trigonometric function and the nature of rotation? BCB？ =60? , and then use the arc length formula.

Answer: solution: ∫In△ABC,? ACB=90？ ,? ABC=30？ ，AB=2，

? cos30？ = ,

? BC=ABcos30？ =2? = ,

∵ Rotate △ABC 60 counterclockwise around the right-angled vertex C? Get △A？ b？ c？ ,

BCB？ =60? ,

? The path length from point B to point B is: =? .

Therefore, choose: B.

Comments: This question mainly examines the nature of rotation and the application of arc length formula, and concludes that the path shape of point B is the key to solving the problem.

6. Use the central angle 120? If a sector with a radius of 3 is the side of a cone, the radius of the bottom of the cone is ()

A.2？ 1

Test Center: Calculation of Cone

Analysis: it is easy to get the arc length of the sector, divided by 2? Is the radius of the base of the cone.

Solution: Solution: The arc length of the sector = =2? ,

Therefore, the radius of the bottom of the cone is 22? = 1.

So choose B.

Comments: investigate the arc length formula of the sector; Formula of circumference of circle; The knowledge points used are: the arc length of the cone is equal to the circumference of the bottom.

7. If the radius of a sector is 8cm and the arc length is cm, the central angle of the sector is ().

A.60? B. 120？ C. 150？ D. 180？

Test center: calculating arc length

Analysis: Let the central angle of the sector be x? According to the arc length formula, we can get: =, and then we can solve the equation.

Solution: let the central angle of the sector be x? According to the arc length formula: =,

Solution: n= 120,

Therefore, choose: B.

Comments: This question mainly examines the calculation of arc length. The key is to master the calculation formula of arc length: l=.

8. As shown in the figure,,, and are all four different circular arcs with O point as the center, with degrees of 60? G is on OA, and C and E are on AG. If AC=EG, OG= 1 and AG=2, what is the sum of the two arc lengths? ( )

A.？ B.4？ 3 C.3？ 2 D.8？ five

Analysis: let AC=EG=a, use a to represent CE = 2-2A, CO = 3-A, EO= 1+a, and then calculate with the formula of sector arc length.

Solution: let AC=EG=a, ce = 2-2a, co = 3-a, EO= 1+a,

+=2? (3﹣a)？ 60? 360? +2? ( 1+a)？ 60? 360? =? 6 (3﹣a+ 1+a)= 4？ 3.

So choose B.

Comments: This question examines the calculation of arc length, and being familiar with the calculation formula of arc length is the key to solving the problem.

9. A piece with a central angle of 45? Cut the fan-shaped cardboard and the circular cardboard into squares as shown in the figure, and the side length is 1, then the area ratio of the fan-shaped cardboard and the circular cardboard is.

A.2 B. 5C.3 D.6

Answer a.

analyse

So choose a.

Test site: 1. Judgement and properties of isosceles right triangle: 2. Pythagorean theorem; 3. Calculation of sector area and circle area.

10. If the generatrix length of the cone is 4 and the bottom radius is 2, then the side area of the cone is ().

A.6? B. 8？ C. 12？ D. 16？

Test Center: Calculation of Cone

Special topic: calculation problems.

Analysis: According to the formula that the side development diagram of the cone is a sector, the arc length of this sector is equal to the circumference of the bottom of the cone, and the radius of the sector is equal to the generatrix length of the cone and the area of the sector.

Solution: Solution: lateral area of this cone =? 4? 22=8? .

So choose B.

Comments: This topic examines the calculation of the cone: the lateral expansion of the cone is a sector, the arc length of this sector is equal to the circumference of the bottom of the cone, and the radius of the sector is equal to the length of the generatrix of the cone.

1 1. The radius of the lateral expansion mode of the cone is 8cm and the central angle is 120? Fan, the radius of the bottom of this cone is ()

A.B. 1 cm c. 3 cm d. 4 cm

Test center: calculating arc length ..

Topic: the finale.

Analysis: Use arc length formula and circle circumference formula to solve.

Solution: solution: let the radius of the bottom of this cone be r,

According to the side development diagram of the cone, the arc length of the sector is equal to the circumference of the cone bottom.

2? r=，

r= cm。

So choose a.

Comments: The side development of the cone is a sector, the arc length of this sector is equal to the circumference of the bottom of the cone, and the radius of the sector is equal to the length of the cone generatrix. In this question, the arc length of the sector is equal to the circumference of the cone bottom, and the equation is solved.

12. A conical crystal ornament, the length of the bus is 10cm, the diameter of the bottom circle is 5cm, and point A is a point on the circumference of the bottom of the cone. Starting from point A, wrap a ribbon around the side of the cone and return to point A, then how many centimeters should the ribbon use at least (the overlap at the interface is ignored) ().

A. 10? cm B. 10 cm C. 5？ 5 cm in diameter

Test center: plane expansion-the shortest path problem; Calculation of cone ..

Analysis: the arc length of the cone-side expansion diagram is equal to the circumference of the bottom circle, and then the degree of the central angle of the sector is calculated, and then AA? Length.

Answer: solution: from the meaning of the question: OA=OA? = 10cm，

= =5? ,

Solution: n=90? ,

AOA？ =90? ,

? AA？ = = 10 (cm),

Therefore, choose: B.

Comments: This topic mainly investigates the shortest path problem of plane expansion diagram and draws a conclusion? AOA？ Degree is the key to solve the problem.

13. As shown in the figure, in 4? In a square grid of 4, the side length of each small square is 1. If △AOC rotates 90 clockwise around point O? If △BOD is obtained, the length of is ()

A.？ B6？ C. 3？ D. 1.5？

Test center: the nature of rotation; Calculation of arc length.

Analysis: According to the arc length formula, the solution can be obtained.

Answer: The length of the solution = = 1.5? .

So choose D.

Comments: This question examines the nature of rotation, the calculation of arc length, and memorizing the formula of arc length is the key to solving problems.

14. Central angle 120? Is the arc length 12? The sector radius of is ()

A.6 B. 9 C. 18 D. 36

Test center: arc length calculation.

Analysis: According to the arc length formula l= calculation.

Solution: Let the sector radius be r. 。

According to the formula l= arc length,

Get: 12? = ,

The solution is r= 18,

So choose: C.

Comments: This question examines the calculation of arc length. Reciting formulas is the key to solving problems.