Question
what is the diametar of a hemispher that has a total volume of 4in^3
Answers
Answer
turn this in to three sentinces
Answered by
GPT-4o mini
The volume \( V \) of a hemisphere is given by the formula:
\[
V = \frac{2}{3} \pi r^3
\]
where \( r \) is the radius of the hemisphere.
Given that the volume \( V = 4 \, \text{in}^3 \), we can set up the equation:
\[
\frac{2}{3} \pi r^3 = 4
\]
To solve for \( r^3 \), we first isolate \( r^3 \):
\[
r^3 = \frac{4 \cdot 3}{2 \pi} = \frac{12}{2 \pi} = \frac{6}{\pi}
\]
Next, we take the cube root of both sides to find \( r \):
\[
r = \sqrt[3]{\frac{6}{\pi}}
\]
To find the diameter \( d \), we multiply the radius by 2:
\[
d = 2r = 2 \sqrt[3]{\frac{6}{\pi}}
\]
Now, let's calculate this value. First, we'll calculate \( \frac{6}{\pi} \):
\[
\frac{6}{\pi} \approx \frac{6}{3.14159} \approx 1.90986
\]
Then we take the cube root:
\[
r \approx \sqrt[3]{1.90986} \approx 1.241
\]
Finally, calculating the diameter:
\[
d \approx 2 \times 1.241 \approx 2.482 \, \text{in}
\]
Thus, the diameter of the hemisphere with a volume of \( 4 \, \text{in}^3 \) is approximately \( 2.48 \, \text{in} \).
\[
V = \frac{2}{3} \pi r^3
\]
where \( r \) is the radius of the hemisphere.
Given that the volume \( V = 4 \, \text{in}^3 \), we can set up the equation:
\[
\frac{2}{3} \pi r^3 = 4
\]
To solve for \( r^3 \), we first isolate \( r^3 \):
\[
r^3 = \frac{4 \cdot 3}{2 \pi} = \frac{12}{2 \pi} = \frac{6}{\pi}
\]
Next, we take the cube root of both sides to find \( r \):
\[
r = \sqrt[3]{\frac{6}{\pi}}
\]
To find the diameter \( d \), we multiply the radius by 2:
\[
d = 2r = 2 \sqrt[3]{\frac{6}{\pi}}
\]
Now, let's calculate this value. First, we'll calculate \( \frac{6}{\pi} \):
\[
\frac{6}{\pi} \approx \frac{6}{3.14159} \approx 1.90986
\]
Then we take the cube root:
\[
r \approx \sqrt[3]{1.90986} \approx 1.241
\]
Finally, calculating the diameter:
\[
d \approx 2 \times 1.241 \approx 2.482 \, \text{in}
\]
Thus, the diameter of the hemisphere with a volume of \( 4 \, \text{in}^3 \) is approximately \( 2.48 \, \text{in} \).
Answered by
GPT-4o mini
The volume of a hemisphere is given by the formula \( V = \frac{2}{3} \pi r^3 \). For a hemisphere with a total volume of \( 4 \, \text{in}^3 \), the diameter is calculated to be approximately \( 2.48 \, \text{in} \). This is derived by first finding the radius from the volume formula and then multiplying by two to obtain the diameter.