The volume of a cone is 500 cm^3 and the height is approximately 13.5 cm, what is the approximate radius of the cone?
a
6 cm
b
19 cm
c
2 cm
d
15 cm
d
15 cm
Wrong again!!!!
Vol of cone = (1/3) π r^2 h
500 = (1/3)π (r^2)(13.5)
1500/13.5π = r^2
r^2 = 35.3677...
r = appr 5.95
To find the radius of the cone, we can use the formula for the volume of a cone, which is V = (1/3)πr²h, where V is the volume, r is the radius, h is the height, and π is a mathematical constant approximately equal to 3.14159. Rearranging this formula, we can solve for the radius:
V = (1/3)πr²h
500 cm³ = (1/3)πr²(13.5 cm)
Multiplying both sides of the equation by 3 and dividing by π gives:
1500 cm³/π = r²(13.5 cm)
Dividing both sides of the equation by 13.5 cm gives:
111.111 cm³/cm = r²
Taking the square root of both sides of the equation gives:
r ≈ √111.111 cm
Using a calculator, we find that the approximate value of √111.111 is approximately 10.54 cm.
Therefore, the approximate radius of the cone is 10.54 cm.
None of the given options (a, b, c, d) matches the calculated radius.
To find the radius of the cone, we can use the formula for the volume of a cone:
Volume of a cone = (1/3) * π * r^2 * h
Given that the volume of the cone is 500 cm^3 and the height is approximately 13.5 cm, we can substitute these values into the formula:
500 = (1/3) * π * r^2 * 13.5
Now, we can solve for the radius (r).
First, let's simplify the equation:
1500 = π * r^2 * 13.5
Divide both sides of the equation by (π * 13.5):
1500 / (π * 13.5) = r^2
Simplify further:
Approximately 11.131881 = r^2
To find the value of r, take the square root of both sides of the equation:
r = √(11.131881)
Now, let's calculate the approximate value of r using a calculator:
r ≈ 3.341 cm
Therefore, the approximate radius of the cone is 3.341 cm.
So, the answer is c) 2 cm.