A right circular cone stands on a hemisphere. The base radius of the cone is equal to the radius of the hemisphere. If the radius of the cone is 10cm and it’s height is 15cm. Calculate to three significant figures the total volume of the solid.
v = 2/3 πr^3 + 1/3 πr^2 h
To find the total volume of the solid, we need to find the volumes of the cone and the hemisphere, and then add them together.
The volume of a cone is given by the formula: V_cone = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height of the cone.
In this case, the radius of the cone is given as 10 cm and the height is given as 15 cm. So, substituting these values into the formula:
V_cone = (1/3) * π * (10 cm)^2 * 15 cm
V_cone ≈ 1/3 * 3.14159 * (10 cm)^2 * 15 cm
V_cone ≈ 1570.796 cm^3
Now, let's calculate the volume of the hemisphere. The volume of a hemisphere is given by the formula: V_hemisphere = (2/3) * π * r^3, where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is also given as 10 cm. So, substituting this value into the formula:
V_hemisphere = (2/3) * 3.14159 * (10 cm)^3
V_hemisphere ≈ 2/3 * 3.14159 * (10 cm)^3
V_hemisphere ≈ 4188.79 cm^3
Finally, we can find the total volume of the solid by adding the volume of the cone and the volume of the hemisphere:
Total volume = V_cone + V_hemisphere
Total volume ≈ 1570.796 cm^3 + 4188.79 cm^3
Total volume ≈ 5759.586 cm^3
Rounded to three significant figures, the total volume of the solid is approximately 5.76 × 10^3 cm^3.
To calculate the total volume of the solid, we need to find the volume of the cone and the volume of the hemisphere.
Volume of a cone formula:
V_cone = (1/3) * π * r^2 * h
Volume of a hemisphere formula:
V_hemisphere = (2/3) * π * r^3
Given information:
Cone radius (r) = 10 cm
Cone height (h) = 15 cm
First, let's calculate the volume of the cone:
V_cone = (1/3) * π * 10^2 * 15
V_cone ≈ 1570.79633 cm^3 (rounded to three significant figures)
Now, let's calculate the volume of the hemisphere. Since the radius of the cone is equal to the radius of the hemisphere:
Hemisphere radius (r) = 10 cm
V_hemisphere = (2/3) * π * 10^3
V_hemisphere ≈ 2094.3951 cm^3 (rounded to three significant figures)
To calculate the total volume, we add the volumes of the cone and the hemisphere:
Total volume = V_cone + V_hemisphere
Total volume ≈ 1570.79633 cm^3 + 2094.3951 cm^3
Total volume ≈ 3665.19143 cm^3 (rounded to three significant figures)
Therefore, the total volume of the solid is approximately 3665.19143 cm^3.