Sondra has a conical bird feeder with a circular top. The volume of the bird feeder is 153.86 cubic inches. The height of the feeder is 12 inches. What is radius of the top? Use 3.14 for mc019-1.jpg. Round the answer to the nearest tenth.
V = π * r² * (h/3)
153.86 = 3.14 * r^2 * 4
153.86 = 12.56 * r^2
153.86/12.56 = r^2
12.25 = r^2
3.5 = r
To find the radius of the top of the bird feeder, we can use the formula for the volume of a cone:
Volume = 1/3 * π * r^2 * h
where π is approximately 3.14, r is the radius of the top, and h is the height of the cone.
In this case, we know the volume of the bird feeder is 153.86 cubic inches and the height is 12 inches. Plugging these values into the formula, we get:
153.86 = 1/3 * 3.14 * r^2 * 12
To solve for the radius, we can rearrange the equation:
r^2 = (3 * 153.86) / (3.14 * 12)
r^2 ≈ 38.93
To find the radius, we take the square root of both sides:
r ≈ √38.93
r ≈ 6.2
Rounding to the nearest tenth, the radius of the top of the bird feeder is approximately 6.2 inches.
To find the radius of the top of the conical bird feeder, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
In this case, we know the volume (V) is 153.86 cubic inches, the height (h) is 12 inches, and we need to find the radius (r) of the top.
We'll start by rearranging the formula to solve for r:
r^2 = (3 * V) / (π * h)
Now we can substitute the given values into the formula:
r^2 = (3 * 153.86) / (3.14 * 12)
Simplifying the calculation:
r^2 = 463.58 / 37.68
r^2 ≈ 12.29
To find the radius (r), we take the square root of both sides of the equation:
r ≈ √12.29
r ≈ 3.5
Rounding the answer to the nearest tenth, the radius of the top of the bird feeder is approximately 3.5 inches.