Asked by uggs
What is the approximate radius of a sphere with a volume of 34 cm3?
A.
4 cm
B.
2 cm
C.
8 cm
D.
6 cm
A.
4 cm
B.
2 cm
C.
8 cm
D.
6 cm
Answers
Answered by
GPT-4o mini
To find the radius of a sphere given its volume, we can use the formula for the volume of a sphere:
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius. We are given that the volume \( V \) is 34 cm³, so we can set up the equation:
\[
34 = \frac{4}{3} \pi r^3
\]
To solve for \( r \), first multiply both sides by \( \frac{3}{4} \):
\[
r^3 = \frac{34 \times 3}{4 \pi}
\]
Calculating that step by step:
1. Calculate \( 34 \times 3 = 102 \)
2. Then, \( \frac{102}{4} = 25.5 \)
3. Now divide by \( \pi \): \( \frac{25.5}{\pi} \approx \frac{25.5}{3.14} \approx 8.13 \)
Now, we need to take the cube root to find \( r \):
\[
r \approx \sqrt[3]{8.13} \approx 2.0 \, \text{cm}
\]
Thus, the approximate radius of the sphere is:
**B. 2 cm**
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius. We are given that the volume \( V \) is 34 cm³, so we can set up the equation:
\[
34 = \frac{4}{3} \pi r^3
\]
To solve for \( r \), first multiply both sides by \( \frac{3}{4} \):
\[
r^3 = \frac{34 \times 3}{4 \pi}
\]
Calculating that step by step:
1. Calculate \( 34 \times 3 = 102 \)
2. Then, \( \frac{102}{4} = 25.5 \)
3. Now divide by \( \pi \): \( \frac{25.5}{\pi} \approx \frac{25.5}{3.14} \approx 8.13 \)
Now, we need to take the cube root to find \( r \):
\[
r \approx \sqrt[3]{8.13} \approx 2.0 \, \text{cm}
\]
Thus, the approximate radius of the sphere is:
**B. 2 cm**