The volume of a cone is 27 cm3 . What is the volume of a cylinder that shares the same radius and height as the cone?(1 point) cm3
The volume of a cone can be calculated using the formula Vcone = (1/3)πr²h, where r is the radius of the cone and h is the height of the cone.
Since the volume of the cone is given as 27 cm³, we can write the equation as 27 = (1/3)πr²h.
To find the volume of the cylinder with the same radius and height as the cone, we need to use the formula Vcylinder = πr²h.
Since the radius and height of the cylinder are the same as the cone, we can substitute the value of h from the cone equation into the cylinder equation.
So, the volume of the cylinder is Vcylinder = πr²((3 * 27) / πr²) = 81 cm³.
Therefore, the volume of the cylinder is 81 cm³.
thx
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To find the volume of the cylinder that shares the same radius and height as the cone, you need to know the formula for the volume of a cone and the formula for the volume of a cylinder.
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant (approximately equal to 3.14159), r is the radius of the base of the cone, and h is the height of the cone.
Since the cone has a volume of 27 cm^3, we can substitute this value into the volume formula and solve for r^2 * h:
27 = (1/3) * π * r^2 * h.
Now, we can use the formula for the volume of a cylinder to find the volume of the cylinder with the same radius and height as the cone. The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume, π is a mathematical constant, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Since the cylinder shares the same radius and height as the cone, we can substitute the value of r^2 * h that we found earlier into the volume formula for the cylinder:
V = π * r^2 * h = π * (27 / (1/3)).
Now, solving this equation will give us the volume of the cylinder in terms of cm^3. By multiplying 27 by 3 and multiplying the result by π, we can find the volume of the cylinder.