Question

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

Answer 1

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

Answer 2

Thanks

Answer 3

good solving, they are actually the answers

Answer 4

WOW,I think i understand it better now

Answer 5

Nice workings

Answer 6

The diagram to the slant height

Answer 7

🖒9 👎1

Answer 8

Amazing I♥️♥️it

Answer 9

I don't understand

Answer 10

Wow I wish I am a mathematician

Answer 11

Thanks for the solution. The diagram would have make it clearer and a split of the question into (a) -(d)

Answer 12

Please show your working
I dont understand it

Answer 13

Sure! Can you specify which question or problem you need help with?

Answer 14

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

Answer 15

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.