What is the radius of a hemisphere with a volume of 7810cm^(3), to the nearest tenth of a centimeter? Answer: cm

Understand Volume Formula: We know the formula for the volume of a hemisphere is $ V = \frac{2}{3}\pi r^3 $, where $ V $ is the volume and $ r $ is the radius. We are given the volume $ V = 7810 $ cm³ and we need to find the radius $ r $.Rearrange Formula: First, we rearrange the formula to solve for $ r $. This gives us $ r^3 = \frac{3V}{2\pi} $.Plug in Values: Next, we plug in the given volume and the approximate value of $ \pi \approx 3.14 $ into the rearranged formula: $ r^3 = \frac{3 \times 7810}{2 \times 3.14} $.Calculate Inside Cube Root: Now, we calculate the value inside the cube root: $ r^3 = \frac{23430}{6.28} $.Perform Division: Performing the division, we get $ r^3 \approx 3730.573248407643 $.Find Radius: To find the radius $ r $, we take the cube root of the result: $ r \approx \sqrt[3]{3730.573248407643} $.Calculate Approximate Radius: Using a calculator, we find that $ r \approx 15.5 $ cm to the nearest tenth of a centimeter.

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What is the radius of a hemisphere with a volume of
7810cm^(3), to the nearest tenth of a centimeter?
Answer:
cm

What is the radius of a hemisphere with a volume of $7810 \mathrm{~cm}^{3}$ , to the nearest tenth of a centimeter? $\newline$ Answer: $\mathrm{cm}$

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Full solution

Q. What is the radius of a hemisphere with a volume of

7810 \mathrm{~cm}^{3}

, to the nearest tenth of a centimeter?

\newline

Answer:

\mathrm{cm}

Understand Volume Formula: We know the formula for the volume of a hemisphere is $V = \frac{2}{3}\pi r^3$ , where $V$ is the volume and $r$ is the radius. We are given the volume $V = 7810$ cm³ and we need to find the radius $r$ .
Rearrange Formula: First, we rearrange the formula to solve for $r$ . This gives us $r^3 = \frac{3V}{2\pi}$ .
Plug in Values: Next, we plug in the given volume and the approximate value of $\pi \approx 3.14$ into the rearranged formula: $r^3 = \frac{3 \times 7810}{2 \times 3.14}$ .
Calculate Inside Cube Root: Now, we calculate the value inside the cube root: $r^3 = \frac{23430}{6.28}$ .
Perform Division: Performing the division, we get $r^3 \approx 3730.573248407643$ .
Find Radius: To find the radius $r$ , we take the cube root of the result: $r \approx \sqrt[3]{3730.573248407643}$ .
Calculate Approximate Radius: Using a calculator, we find that $r \approx 15.5$ cm to the nearest tenth of a centimeter.