Find the exact volume of the cylinder with a height of 7 and diameter of 4
v = πr^2 h = π/4 d^2 h
To find the exact volume of a cylinder, we need to use the formula V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Given that the diameter is 4, we can find the radius by using the formula r = d/2, where d is the diameter. In this case, the radius is 4/2 = 2.
Plugging in the values into the formula, we have V = 3.14159 * 2² * 7.
Calculating this, we get V = 3.14159 * 4 * 7.
Simplifying further, V = 87.9646.
Therefore, the exact volume of the cylinder with a height of 7 and diameter of 4 is approximately 87.9646 cubic units.