Question
hat is the height of the cone below?
A cone with base of 18 centimeters squared and volume of 90 centimeters cubed.
5 cm
6 cm
15 cm
30 cm
A cone with base of 18 centimeters squared and volume of 90 centimeters cubed.
5 cm
6 cm
15 cm
30 cm
Answers
GPT 3.5
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height.
Given that the base of the cone has an area of 18 cm^2, we can find the radius using the formula for the area of a circle, A = πr^2.
18 = πr^2
r^2 = 18/π
r ≈ √(18/π) ≈ 2.39 cm
Now we can substitute the radius into the volume formula and solve for the height:
90 = (1/3)π(2.39)^2h
90 = (1/3)π(5.68)h
90 = 5.68πh
h ≈ 15 cm
Therefore, the height of the cone is approximately 15 cm.
So the correct answer is: 15 cm
Given that the base of the cone has an area of 18 cm^2, we can find the radius using the formula for the area of a circle, A = πr^2.
18 = πr^2
r^2 = 18/π
r ≈ √(18/π) ≈ 2.39 cm
Now we can substitute the radius into the volume formula and solve for the height:
90 = (1/3)π(2.39)^2h
90 = (1/3)π(5.68)h
90 = 5.68πh
h ≈ 15 cm
Therefore, the height of the cone is approximately 15 cm.
So the correct answer is: 15 cm