a paper cone has a base diameter of 8cm a height of 3cm.
a)caculate the volume of the cone in terms of pie
b)if the cone is cut and opened out into the sector of a circle.what is the angle of the sector
a) v = ⅓ π r² h = 16 π
b) the radius of the circle is 5 cm
... √[(8/2)² + 3²] = 5
Θ = 2 π * 8 / 10
9 in height
6in
a) To calculate the volume of a cone in terms of pi, we can use the formula:
Volume of cone = (1/3) * pi * r^2 * h
Where:
- r is the radius of the base (half of the diameter)
- h is the height of the cone
In this case, the base diameter is 8 cm, so the radius would be half of that, which is 4 cm. The height of the cone is given as 3 cm.
Substituting these values into the formula, we get:
Volume of cone = (1/3) * pi * (4 cm)^2 * 3 cm
= (1/3) * pi * 16 cm^2 * 3 cm
= (1/3) * pi * 48 cm^3
= 16 pi cm^3
Therefore, the volume of the cone in terms of pi is 16 pi cm^3.
b) To find the angle of the sector when the cone is cut and opened out, we need to consider that the curved surface of the cone forms the circumference of the base of the sector. The circumference of a circle is calculated using the formula:
Circumference of circle = 2 * pi * r
In this case, the radius of the base is 4 cm. So, the circumference would be:
Circumference of circle = 2 * pi * 4 cm
= 8 pi cm
Since the curved surface of the cone has been cut and opened out to form the circumference of the sector, the angle of the sector can be calculated as:
Angle of sector = (Circumference of circle / Circumference of a full circle) * 360 degrees
Substituting the values, we get:
Angle of sector = (8 pi cm / 8 pi cm) * 360 degrees
= 360 degrees
Therefore, the angle of the sector is 360 degrees.