A frustum is formed when a plane that is parallel to a cone's base cuts off the upper portion, as shown below. A cone is shown. The top part of the cone is cut off to form a frustum. The frustum has a height of 6 and a radius of 4. The cone has a height of 3 and a radius of 2. What is the volume of the frustum? Leave the answer in terms of π.
Answers
Answer:
44
Explanation:
just did it edg 2021
The volume of the frustum of the cone is V = 44π units³
What is a Cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Surface area of the cone = πr ( l + r )
where l = √ ( b² + r² )
Given data ,
Let the volume of the smaller cone be V₁
Let the volume of the entire cone be V₂
And , the volume of frustum is V = V₂ - V₁
Let the radius of the smaller cone be r
Now , the value of r = 2 units
The height of the smaller cone h = 3 units
So , the volume V₁ = ( 1/3 ) πr²h
V₁ = ( 1/3 )π ( 2 )² ( 3 )
V₁ = 4 units³
And , volume of the entire cone be V₂ = ( 1/3 )π ( 4 )² ( 9 )
V₂ = 48π units³
So , the volume of frustum is V = 48π units³ - 4 units³
V = 44π units³
Hence , the volume of the frustum is 44π units³
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The complete question is attached below :
A frustum is formed when a plane that is parallel to a cone's base cuts off the upper portion, as shown below. A cone is shown. The top part of the cone is cut off to form a frustum. The frustum has a height of 6 and a radius of 4. The cone has a height of 3 and a radius of 2. What is the volume of the frustum? Leave the answer in terms of π.
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Is correct answer
I don't know properly
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Just finished the questions and got it right :)
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