What is the volume of a hemisphere with a radius of 3 m?

What is the volume of a hemisphere with a radius of 3 m?

• A. 14.137
• B. 28.274
• C. 84.823
• D. 56.55

Answer: (D)

To find the volume of a hemisphere, you can use the formula: \[ V = \frac{2}{3} \pi r^3 \] Where \( V \) is the volume and \( r \) is the radius of the hemisphere. Given a radius of 3 meters, you can substitute this value into the formula: 1. Calculate \( r^3 \): \[ r^3 = 3^3 = 27 \] 2. Now, substitute \( r^3 \) back into the volume formula: \[ V = \frac{2}{3} \pi \times 27 \] 3. Simplify the calculation: \[ V = \frac{54\pi}{3} = 18\pi \] 4. Now, using the approximate value of \(\pi \approx 3.14\): \[ V \approx 18 \times 3.14 = 56.52 \] Since the choices are often rounded, this volume rounds to approximately 56.55 cubic meters. Thus, the correct answer reflects the accurate application of the formula for the volume of a hemisphere

To find the volume of a hemisphere, you can use the formula:

[

V = \frac{2}{3} \pi r^3

]

Where ( V ) is the volume and ( r ) is the radius of the hemisphere. Given a radius of 3 meters, you can substitute this value into the formula:

1. Calculate ( r^3 ):

[

r^3 = 3^3 = 27

]

2. Now, substitute ( r^3 ) back into the volume formula:

[

V = \frac{2}{3} \pi \times 27

]

3. Simplify the calculation:

[

V = \frac{54\pi}{3} = 18\pi

]

4. Now, using the approximate value of (\pi \approx 3.14):

[

V \approx 18 \times 3.14 = 56.52

]

Since the choices are often rounded, this volume rounds to approximately 56.55 cubic meters. Thus, the correct answer reflects the accurate application of the formula for the volume of a hemisphere