Asked by Love
a paper cone has a base diameter of 8cm and a height of 3cm.calculate the volume of the cone in terms of pie and make a sketch of the cone and hence use Pythagoras theorem to calculate its slant height and calculate the curve surface area of the cone in terms of pie and if the cone is cut and open out into the sector of a circle. what is the angle of the sector
Answers
Answered by
Reiny
Radius of base = 4 cm, height = 3 cm
Volume = (1/3)π(4^2)(3) = 16π cm^3
slant height --- s
s^2 = 4^2 + 3^2
s = 5 , (did your recognize the standard 3-4-5 right angled triangle?)
So the radius of the sector is 5 and the arclength is the circumference of the base of the cone.
Circumference of base = arc of sector = 8π cm
circumference of circle containing our sector = 10π cm, so the area of the sector is 4/5 the area of the big circle
area of sector = (4/5)π(5^2) = 20π cm^2
Of course I could have just used the formula
lateral area of cone = πrl, where r is the radius of the cone and l is the slant height
= π(4)(5) = 20π
for the sector angle:
sector-angle/360 = 8π/10π = 4/5
sector angle = 288°
check my arithmetic
Volume = (1/3)π(4^2)(3) = 16π cm^3
slant height --- s
s^2 = 4^2 + 3^2
s = 5 , (did your recognize the standard 3-4-5 right angled triangle?)
So the radius of the sector is 5 and the arclength is the circumference of the base of the cone.
Circumference of base = arc of sector = 8π cm
circumference of circle containing our sector = 10π cm, so the area of the sector is 4/5 the area of the big circle
area of sector = (4/5)π(5^2) = 20π cm^2
Of course I could have just used the formula
lateral area of cone = πrl, where r is the radius of the cone and l is the slant height
= π(4)(5) = 20π
for the sector angle:
sector-angle/360 = 8π/10π = 4/5
sector angle = 288°
check my arithmetic
Answered by
Eirene
Thanks
Answered by
Brianna
good solving, they are actually the answers
Answered by
JANE
WOW,I think i understand it better now
Answered by
Frosh
Nice workings
Answered by
Anonymous
The diagram to the slant height
Answered by
Ola
🖒9 👎1
Answered by
Michelle
Amazing I♥️♥️it
Answered by
Emmanuel
I don't understand
Answered by
Margret
Wow I wish I am a mathematician
Answered by
Michael
Thanks for the solution. The diagram would have make it clearer and a split of the question into (a) -(d)
Answered by
Ajoke
Please show your working
I dont understand it
I dont understand it
Answered by
Princess
a) Volume=⅓πr²h
=⅓π×4×4×3
=16πcm³
b)By Pythagoras
3²+4²= l²
9+16= l²
l=√25
l= 5cm.
c) Curved Surface Area=πrl
=π×4×5
=20πcm²
=⅓π×4×4×3
=16πcm³
b)By Pythagoras
3²+4²= l²
9+16= l²
l=√25
l= 5cm.
c) Curved Surface Area=πrl
=π×4×5
=20πcm²
Answered by
Bot
Sure! Can you specify which question or problem you need help with?
Answered by
GPT 3.5
To determine the angle of the sector when the cone is cut and opened out into the sector of a circle, we can use the ratio between the circumference of the base of the cone and the circumference of the circle.
The circumference of the base of the cone is equal to the circumference of the sector.
The circumference of the base of the cone is given by:
Circumference = 2πr = 2π(4) = 8π cm
The circumference of the circle containing the sector is given by:
Circumference = 2πr' = 2π(5) = 10π cm
The angle of the sector is equal to the ratio of the circumference of the base of the cone to the circumference of the circle containing the sector, multiplied by 360 degrees.
Angle of sector = (Circumference of cone / Circumference of circle) * 360 degrees
= (8π / 10π) * 360 degrees
= (4/5) * 360 degrees
= 288 degrees
Therefore, the angle of the sector is 288 degrees.
The circumference of the base of the cone is equal to the circumference of the sector.
The circumference of the base of the cone is given by:
Circumference = 2πr = 2π(4) = 8π cm
The circumference of the circle containing the sector is given by:
Circumference = 2πr' = 2π(5) = 10π cm
The angle of the sector is equal to the ratio of the circumference of the base of the cone to the circumference of the circle containing the sector, multiplied by 360 degrees.
Angle of sector = (Circumference of cone / Circumference of circle) * 360 degrees
= (8π / 10π) * 360 degrees
= (4/5) * 360 degrees
= 288 degrees
Therefore, the angle of the sector is 288 degrees.
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