The formula for finding the volume of a cone is \large V=\frac{1}{3}\pi r^2h. 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
2 cm
b
19 cm
c
15 cm
d
6 cm
c
15 cm
AAAaannndd the bot gets it wrong yet again!
To find the radius of the cone, we can rearrange the formula for the volume of a cone:
V = (1/3)πr^2h
To find the radius, we can isolate 'r' by dividing both sides of the equation by (1/3)πh:
r^2 = V / ((1/3)πh)
r^2 = (3V) / (πh)
r = √( (3V) / (πh) )
Given that V = 500 cm^3 and h = 13.5 cm, we can substitute these values into the equation:
r = √( (3*500) / (π*13.5) )
r ≈ √( 1500 / 42.4 )
r ≈ √( 35.38 )
r ≈ 5.95
Therefore, the approximate radius of the cone is 6 cm (option d).
To find the radius of the cone, we can rearrange the formula for volume to solve for the radius.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, h is the height, and π is a mathematical constant approximately equal to 3.14.
Given that the volume is 500 cm^3 and the height is approximately 13.5 cm, we can substitute these values into the formula:
500 = (1/3)πr^2(13.5)
Now, let's solve for r.
First, multiply both sides of the equation by 3 to get rid of the fraction:
1500 = πr^2(13.5)
Next, divide both sides of the equation by π(13.5):
1500 / (π * 13.5) = r^2
Now, calculate the value on the left side of the equation:
r^2 ≈ 1500 / (3.14 * 13.5)
r^2 ≈ 35.59
To find the radius, take the square root of both sides of the equation:
r ≈ √35.59
Now, we can approximate the value of r:
r ≈ 5.97 cm
Therefore, the approximate radius of the cone is 6 cm (approximately).
Hence, the answer is (d) 6 cm.