THE VOLUME OF A CONE IS 20 PI CUBIC METERS. WHAT IS THE VOLUME OF A CYLINDER HAVING THE SAME BASE AND SAME HEIGHT?
60
cone: volume is 1/3 base * height
cylinder: volume is base * height
so, what do you think?
1/3
To find the volume of a cylinder having the same base and height as a given cone, you need to know the formula for the volume of a cone and the relationship between the volumes of a cone and a cylinder.
The volume of a cone is given by the formula: V = (1/3)πr²h, where V represents the volume, π is a 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 volume of the cone is given as 20π cubic meters. Therefore, we have the equation: 20π = (1/3)πr²h.
Now, let's consider the volume of the cylinder. The volume of a cylinder is given by the formula: V = πr²h, where V represents the volume, π is the same constant as before, r is the radius of the base, and h is the height of the cylinder.
Since the cone and the cylinder have the same base and height, we can substitute the values of r and h from the cone into the formula for the cylinder.
From the equation 20π = (1/3)πr²h, we can identify that r²h is 60. Dividing both sides by π, we get r²h = 60/π.
Now we can substitute this value into the formula for the volume of the cylinder: V = πr²h. Substituting r²h = 60/π, we have V = π(60/π), which simplifies to V = 60 cubic meters.
Therefore, the volume of the cylinder having the same base and height as the given cone is 60 cubic meters.