3. A basket of beads contains 8 red beads, 6 yellow beads, and 6 green beads. A
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Answer:
Volume of the frustum = ⅓πh(4R² - r²)
Step-by-step explanation:
We are to determine the volume of the frustum.
Find attached the diagram obtained from the given information.
Let height of small cone = h
height of the large cone = H
The height of a small cone is a quarter of the height of the large cone:
h = ¼×H
H = 4h
Volume of the frustum = volume of the large cone - volume of small cone
volume of the large cone = ⅓πR²H
= ⅓πR²(4h) = 4/3 ×π×R²h
volume of small cone = ⅓πr²h
Volume of the frustum = 4/3 ×π×R²h - ⅓πr²h
Volume of the frustum = ⅓(4π×R²h - πr²h)
Volume of the frustum = ⅓πh(4R² - r²)
By definition, the volume of a cone is given by:
Where,
r: radius of the circular base
h: height of the cone
Let's define a variable:
x: diameter of the base
We have then that the radio is:
The height is:
Substituting values:
Rewriting:
Answer:
An expression that represents the volume of the cone, in cubic units is:
Where,
r: radius of the circular base
h: height of the cone
Let's define a variable:
x: diameter of the base
We have then that the radio is:
The height is:
Substituting values:
Rewriting:
Answer:
An expression that represents the volume of the cone, in cubic units is: