the volume of a cone is 154cm^3 .if it's radius is 7cm . calculate the height of the cone
22/7*7/1*h/1
154=22h
h=154/22
=7cm
To calculate the height of the cone, we can use the formula for the volume of a cone:
Volume of a Cone = (1/3) * π * r^2 * h
where:
π is a mathematical constant approximately equal to 3.14159.
r is the radius of the base of the cone.
h is the height of the cone.
Given that the volume of the cone is 154 cm^3 and the radius is 7 cm, we can rearrange the formula to solve for the height:
h = (3 * Volume) / (π * r^2)
Now, let's substitute the given values into the formula:
h = (3 * 154 cm^3) / (π * (7 cm)^2)
First, let's square the radius:
h = (3 * 154 cm^3) / (π * 49 cm^2)
Now, let's calculate the value of π to the appropriate number of decimal places:
π ≈ 3.14159
h = (3 * 154 cm^3) / (3.14159 * 49 cm^2)
Next, let's calculate the value inside the parentheses:
h = (462 cm^3) / (153.938 cm^2)
Finally, let's divide the volume by the area:
h ≈ 3.00 cm
Therefore, the height of the cone is approximately 3 cm.