A cylinder has a volume of 83 in3 and is 10 in. tall. What is the radius of the cylinder in inches
since v = pi r^2 h,
83 = pi r^2 (10)
r^2 = 83/(10pi)
r = 1.625 in
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where:
- Volume is the given volume of the cylinder (83 in^3)
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder (unknown)
- h is the height of the cylinder (10 in)
Rearranging the formula, we can solve for the radius (r):
r^2 = Volume / (π * h)
Substituting the given values:
r^2 = 83 in^3 / (π * 10 in)
To find the radius, we need to take the square root of both sides of the equation:
r = √(83 in^3 / (π * 10 in))
Using a calculator or estimating the value of π as 3.14159, we can calculate the radius:
r ≈ √(83 / (3.14159 * 10)) ≈ √2.643415 ≈ 1.626867
Therefore, the radius of the cylinder is approximately 1.63 inches.