Asked by shegster
A sector of a circle subtending an angle 300 degrees at the centre is used to form a cone with base radius 6cm. Find the (a.)radius of the circle (b.)volume of the cone (c.)area of the minor sector of the circle
Answers
Answered by
Reiny
It often helps to see a physical model of the problem
Cut out a circular sector with scissors and form it into a cone.
You will see that the arc length of the sector becomes the circumference of the circular base of the cone
if the cone is to have a radius of 6 cm, then its circumference is 12π cm
You should be familiar with the relation,
arc = rØ for a sector, where Ø is the sector angle in radians
300° to radians --->Ø/2π = 300/360---> Ø = 10π/6
12π = r(10π/6)
r = 12π(6/10π) = 7.2
So our sector must have a radius of 7.2 cm
b) If you look at your model you will see that 72 cm becomes the "slant" length of the cone, so using Pythagoras,
h^2 + 6^2 = 7.2^2 , where h is the height of the cone
h = √15.84
volume = (1/3) base x height
= (1/3)(36π)(√15.84)
= appr 150.04 cm^3
c) area of minor sector....
our needed sector is 5/6 of the circle, so the minor sector would be 1/6 of the area of the circle
area of minor sector = (1/6)π(7.2^2)
= appr 27.14 cm^2
check my arithmetic.
Cut out a circular sector with scissors and form it into a cone.
You will see that the arc length of the sector becomes the circumference of the circular base of the cone
if the cone is to have a radius of 6 cm, then its circumference is 12π cm
You should be familiar with the relation,
arc = rØ for a sector, where Ø is the sector angle in radians
300° to radians --->Ø/2π = 300/360---> Ø = 10π/6
12π = r(10π/6)
r = 12π(6/10π) = 7.2
So our sector must have a radius of 7.2 cm
b) If you look at your model you will see that 72 cm becomes the "slant" length of the cone, so using Pythagoras,
h^2 + 6^2 = 7.2^2 , where h is the height of the cone
h = √15.84
volume = (1/3) base x height
= (1/3)(36π)(√15.84)
= appr 150.04 cm^3
c) area of minor sector....
our needed sector is 5/6 of the circle, so the minor sector would be 1/6 of the area of the circle
area of minor sector = (1/6)π(7.2^2)
= appr 27.14 cm^2
check my arithmetic.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.