A sector of central angle 216 degree is cut from a circle of radius 25 cm and is rolled up into a cone. What are the base radius and height of the cone ? What is its volume
Answers
Step-by-step explanation:
Radius of the circle = R = 25 cm.
angle of the sector = Ф = 216°.
Length of the circular arc cut off from the circle
= 2 π R * Ф/360°
= 2 * 22/7 * 25 * 216/360 cm
= 94.29 cm
The piece is bent into a right circular cone.
So the slanting height s of the cone = radius of circle = R = 25 cm.
s = 25 cm
circumference of the base of the cone = arc length = 94.29 cm
base radius r of the cone = r = 94.29 * 1/2π = 148.17 cm
height of the cone = h = √(s² - r²) = 25² - 148.17²) = -21329.35 cm
Volume of the cone = V = π/3 * r² h
V = 22/7 * 1/3 * 148.17² * -21329.35 cm³
= −1.046355326×10¹³ cm³
hope it helps mark as brilliant.
The radius of the Cone is 15 cm, the height is 20 cm and the volume is 1500π cm³.
Given:
A sector of central angle 216° is cut from a circle of radius 25 cm and is rolled up into a cone.
To find:
What are the base radius and height of the cone? What is its volume?
Solution:
Formula used:
The arc length of the sector is: (Arc Measure / 360°) ⋅ 2πr
From the data,
A sector of central angle 216° is cut from a circle
Length of the sector = [ 216/360 ] × 2π(25) = 30π
Here the sector is formed as a cone
Length of the Arc = Circumference of the base of the cone
Let R be the radius of the cone
=> 30π = 2πR
=> R = 15 cm
∴ The radius of the Cone is 15 cm
Here slant height of the cone will equal the radius of the original circle
Height of the cone can be calculated as follows
Height = √ [ Slant height² - Radius² ]
Height = √25² - 15² = 20 cm
∴ The height of the cone is 20 cm
Using the formula, V = (1/3)πr²h
Volume of cone = (1/3)π(15)²(20) = 1500π cm³
Therefore,
The volume of the cone is 1500π cm³
Learn more at
https://brainly.in/question/54096697
#SPJ3
