Question

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

tip: work backwards

Answer 1

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Answer 2

To find the radius of a cone, we can use the formula for the volume of a cone:

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.

In this case, we are given that V = 477 mm^3 and h = 28.5 mm. Plugging those values into the equation, we have:

477 = (1/3) * π * r^2 * 28.5

We can simplify the equation by multiplying both sides by 3:

3 * 477 = π * r^2 * 28.5

1431 = π * r^2 * 28.5

Dividing both sides by π * 28.5, we have:

1431 / (π * 28.5) = r^2

To find the radius, we need to take the square root of both sides:

√(1431 / (π * 28.5)) = r

Using a calculator, we can evaluate the expression on the right-hand side:

r ≈ 6.006

Therefore, the radius of the cone is approximately 6.006 mm.

Answer 3

Apologies for my mistake in the previous response.

To find the radius of a cone, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

We are given that V = 477 mm^3 and h = 28.5 mm. Plugging in those values, we have:

477 = (1/3) * π * r^2 * 28.5

Multiplying both sides by 3:

1431 = π * r^2 * 28.5

Dividing both sides by π * 28.5:

r^2 = 1431 / (π * 28.5)

Taking the square root of both sides:

r = √(1431 / (π * 28.5))

Using a calculator to evaluate the right-hand side:

r ≈ 6.028

Therefore, the radius of the cone is approximately 6.028 mm.