A cone with a height of a 9 feet in the diameter of 8 feet if this con were doubled, what would be the volume of the new cone
The radius of the original cone is 4 feet (diameter of 8 feet / 2). Using the formula for the volume of a cone, we can calculate the volume of the original cone as:
V = 1/3 * π * r^2 * h
V = 1/3 * π * 4^2 * 9
V = 48π
To find the volume of the new cone, we first need to determine the new dimensions. Doubling the cone means that both the height and the radius will be multiplied by 2. Therefore, the new cone will have:
- a height of 18 feet (original height of 9 feet * 2)
- a radius of 8 feet (original radius of 4 feet * 2)
Using the same formula for volume, we can calculate the volume of the new cone as:
V = 1/3 * π * 8^2 * 18
V = 384π
Therefore, the volume of the new cone is 384π cubic feet.
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To find the volume of a cone, we use the formula V = (1/3) * π * r² * h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
In this case, the given cone has a height of 9 feet and a diameter of 8 feet. To find the radius (r) of the base, we divide the diameter by 2. So, r = 8 feet / 2 = 4 feet.
Now, let's calculate the volume of the original cone:
V₁ = (1/3) * π * (4 feet)² * 9 feet
V₁ = (1/3) * 3.14159 * 16 square feet * 9 feet
V₁ ≈ 150.7963 cubic feet
The volume of the original cone is approximately 150.7963 cubic feet.
To find the volume of the new cone when it is doubled, we can accommodate that the proportion of the volume is doubled as well. So, we can simply multiply the volume of the original cone by 2.
V₂ = 2 * V₁
V₂ ≈ 2 * 150.7963 cubic feet
V₂ ≈ 301.5926 cubic feet
Therefore, the volume of the new cone, when the original cone is doubled, is approximately 301.5926 cubic feet.