The volume of a cylinder is 24pi cubic feet. What is the volume of a cone having same base and same height?
To find the volume of a cone with the same base and height as a given cylinder, you can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Where V is the volume, π is Pi (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
In this case, the volume of the cylinder is given as 24π cubic feet. We can assume that the height of both the cylinder and the cone is the same, so we can write the equation as:
24π = (1/3) * π * r^2 * h
Simplifying the equation:
24 = (1/3) * r^2
Multiply both sides of the equation by 3:
72 = r^2
Take the square root of both sides to find the radius:
r = √(72) = 6√2
Now, we can substitute the value of r back into the volume formula for the cone:
V_cone = (1/3) * π * r^2 * h
= (1/3) * π * (6√2)^2 * h
= (1/3) * π * 72 * h
= 24π * h
Since the height is the same for both the cylinder and the cone, the volume of the cone is also 24π cubic feet.
To find the volume of a cone with the same base and height as a given cylinder, we need to use the formula for the volume of a cone.
The formula for the volume of a cylinder is: V = πr^2h, where V is the volume, r is the radius of the base, and h is the height.
In this case, we are given that the volume of the cylinder is 24π cubic feet. This means V = 24π.
To find the radius (r) and height (h) of the cylinder, we can use the formula for the volume of a cylinder. Rearranging the formula, we get:
V = πr^2h
24π = πr^2h
Since the base of the cone is the same as the base of the cylinder, the radius (r) of the cylinder is equal to the radius (r) of the cone.
We can substitute r^2 from the cylinder equation into the cone formula:
V_cone = (1/3)πr^2h
Now, we can substitute the values we know:
V_cone = (1/3)π( r^2)(h)
V_cone = (1/3)π( r^2)(h) = (1/3)π(r^2)(h)
V_cone = (1/3)π( r^2)(h) = (1/3)π( r^2)(h) = (1/3)(24π)= (1/3) × (8 × 3.14) = 8π/3 cubic feet
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look at the volume formulas. For equal dimensions, pyramids and cones have
v = 1/3 Bh
while prisms and cylinders have v=Bh