What is the surface areo of the cone(hat) and what is the circumference of the base of the cone(hat)? the side of the cone has a angle 144' and a length of 25cm? 1) How do you find the radius?
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write3,002 answers
starTop subjects are Math, Science, and Business
Assuming that you are cutting a sector out of a circle with radius 25 and central angle `144^@` and forming a cone with what is left.
The radius of the circle is the slant height of the cone (length of side) and equals 25. Then the arc length that is left is `216/360=3/5` of the circumference of the original circle. Since the circle had circumference `C=2pir=2pi(25)=50pi` we have the arc length `3/5*50pi=30pi` . This is the circumference of the base of the cone.
The circumference of the base of the cone is `C=2piR` where R is the radius of the cone. So `2piR=30pi==>R=15`
The radius of the base of the cone will be 15cm.
(The circumference of the base is `30pi "cm"` ; the surface area of the cone is the area of the original circle left after removing the sector. Then SA=`216/360pir^2=3/5pi(625)=375pi"cm"^2` )
Related Questions
- What is the length of the side of a cube whose surface area is 384 cm^2.
- 1 Educator Answer
- If the Circumference is 6 ft. What is the radius?
- 1 Educator Answer
- A sector of a circle of radius 8cm subtends a 90 degree angle at the center of the circle. If the...
- 1 Educator Answer
- The radius of a circle is 6 inches. If the central angle is 5pi/3, find the length of the...
- 1 Educator Answer
- The circumference of a circle is equal to 72 pi. Find the radius of this circle.
- 1 Educator Answer
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.