What is the volume of a hemisphere with a diameter of 47.7 in, rounded to the nearest tenth of a cubic inch? Answer Attempt 1 out of 2

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

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

where $$ r $$ is the radius of the hemisphere.

Given that the diameter of the hemisphere is 47.7 inches, we can find the radius by dividing the diameter by 2:

$$ r = \frac{47.7}{2} = 23.85 \text{ inches} $$

Now, we can substitute the value of the radius into the formula to find the volume:

$$ V = \frac{2}{3} \pi (23.85)^3 $$

Let's calculate the volume.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2}{3}\pi \times 23.85^{3}$$
- step1: Convert the expressions:
  $$\frac{2}{3}\pi \left(\frac{477}{20}\right)^{3}$$
- step2: Multiply:
  $$\frac{2\pi }{3}\left(\frac{477}{20}\right)^{3}$$
- step3: Evaluate the power:
  $$\frac{2\pi }{3}\times \frac{477^{3}}{20^{3}}$$
- step4: Rewrite the expression:
  $$\frac{2\pi }{3}\times \frac{477^{3}}{4^{3}\times 5^{3}}$$
- step5: Rewrite the expression:
  $$\frac{2\pi }{3}\times \frac{477^{3}}{2^{6}\times 5^{3}}$$
- step6: Reduce the numbers:
  $$\frac{\pi }{3}\times \frac{477^{3}}{2^{5}\times 5^{3}}$$
- step7: Rewrite the expression:
  $$\frac{\pi }{3}\times \frac{9^{3}\times 53^{3}}{2^{5}\times 5^{3}}$$
- step8: Rewrite the expression:
  $$\frac{\pi }{3}\times \frac{3^{6}\times 53^{3}}{2^{5}\times 5^{3}}$$
- step9: Reduce the numbers:
  $$\pi \times \frac{3^{5}\times 53^{3}}{2^{5}\times 5^{3}}$$
- step10: Multiply:
  $$\frac{\pi \times 243\times 53^{3}}{4000}$$
- step11: Multiply:
  $$\frac{243\times 53^{3}\pi }{4000}$$
The volume of the hemisphere with a diameter of 47.7 inches is approximately 28,413.44 cubic inches.

Rounded to the nearest tenth of a cubic inch, the volume is 28,413.4 cubic inches.
The volume of the hemisphere is approximately 28,413.4 cubic inches.

What is the volume of a hemisphere with a diameter of 47.7 in, rounded to the nearest tenth of a cubic inch? Answer Attempt 1 out of 2

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