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
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