Final answer:
The volume of a hemisphere with a radius of 3 cm is approximately 56.6 cm³ when rounded to the nearest tenth of a cubic centimeter. This is calculated by halving the volume of a sphere with the same radius.
Step-by-step explanation:
Calculating the Volume of a Hemisphere
The question asks for the volume of a hemisphere with a radius of 3 cm. The formula for the volume of a sphere is V = (4/3)πr³, and since a hemisphere is half of a sphere, the formula adapts to V = (1/2)(4/3)πr³. Using a radius (r) of 3 cm, we get V = (1/2)(4/3)π(3 cm)³.
Let's calculate the volume step by step:
- First, calculate the volume of the full sphere using the radius of 3 cm: V = (4/3)π(3³) cm³
- Compute the result: V = (4/3)(π)(27) cm³ = (36π) cm³
- Since we want the volume of the hemisphere, we divide this number by 2: V = (36π/2) cm³ = (18π) cm³
- Finally, we approximate π to 3.142 and round to the nearest tenth: V ≈ 18(3.142) cm³ ≈ 56.6 cm³
Therefore, the approximate volume of the hemisphere is 56.6 cm³, when rounded to the nearest tenth of a cubic centimeter.