A right circular cone stands on a hemisphere. The base radius of the cone is equal to the radius of the hemisphere. If the base radius of the cone is 10 centimeters and its height is 15 centimeters,calculate the total volume of the solid.
cone: 1/3 πr^2 h
hemisphere: 2/3 πr^3
sum: πr^2/3 (h+2r)
Now just plug in your values.
To calculate the total volume of the solid, we first need to find the volumes of the cone and the hemisphere separately, and then add them together.
1. Volume of the cone:
The volume of a cone can be calculated using the formula:
V_cone = (1/3) * π * r^2 * h,
where r is the radius of the base and h is the height.
In this case, the base radius of the cone is 10 centimeters and its height is 15 centimeters.
Thus, substituting the given values into the formula:
V_cone = (1/3) * π * 10^2 * 15.
2. Volume of the hemisphere:
The volume of a hemisphere can be calculated using the formula:
V_hemisphere = (2/3) * π * r^3,
where r is the radius of the hemisphere.
In this case, the base radius of the cone is equal to the radius of the hemisphere, which is 10 centimeters.
Thus, substituting the given value into the formula:
V_hemisphere = (2/3) * π * 10^3.
Now, add the volumes of the cone and the hemisphere to calculate the total volume:
Total Volume = V_cone + V_hemisphere.
Substituting the calculated values of V_cone and V_hemisphere into the equation will give you the total volume of the solid.