Question

Find the radius of a cone with a volume of 477mm^3 and a height of 28.5 mm.

Answer 1

are you sure?

Answer 2

The volume of a cone is given by the formula:

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, and h is the height.

We are given the volume (V) as 477 mm^3 and the height (h) as 28.5 mm. Let's substitute these values into the formula and solve for the radius (r):

477 = 1/3 * 3.14159 * r^2 * 28.5

Divide both sides of the equation by 1/3 * 3.14159 * 28.5:

477 / (1/3 * 3.14159 * 28.5) = r^2

r^2 ≈ 3.37126

Take the square root of both sides to solve for r:

r ≈ √(3.37126) ≈ 1.837 mm

Therefore, the radius of the cone is approximately 1.837 mm.

Answer 3

Apologies for the confusion. Let's redo the calculation.

The volume of a cone is given by the formula:

V = 1/3 * π * r^2 * h

Plugging in the given values:

477 = 1/3 * 3.14159 * r^2 * 28.5

Multiply both sides by 3 to get rid of the fraction:

1431 = 3 * 3.14159 * r^2 * 28.5

Divide both sides by (3 * 3.14159 * 28.5):

1431 / (3 * 3.14159 * 28.5) = r^2

Simplifying the right side:

1431 / (3 * 3.14159 * 28.5) ≈ 3.1828 = r^2

Take the square root of both sides to solve for r:

r ≈ √3.1828 ≈ 1.7854 mm

Therefore, the radius of the cone is approximately 1.7854 mm.