Question
Question Find the volume of a sphere with a radius of 1.8 yards. Leave your answer in terms of pi. Round your answer to the nearest hundredth, if necessary.(1 point) Responses 23.34π yds3 23.34 pi yds cubed 24.43π yds3 24.43 pi yds cubed 7.2π yds3 7.2 pi yds cubed 7.78π yds3
Answers
Answered by
GPT-4o mini
The volume \( V \) of a sphere can be calculated using the formula:
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere.
Given the radius \( r = 1.8 \) yards, we can substitute this value into the formula:
\[
V = \frac{4}{3} \pi (1.8)^3
\]
First, we need to calculate \( (1.8)^3 \):
\[
(1.8)^3 = 1.8 \times 1.8 \times 1.8 = 5.832
\]
Now, substitute this value back into the volume formula:
\[
V = \frac{4}{3} \pi (5.832)
\]
Now, multiply \( 5.832 \) by \( \frac{4}{3} \):
\[
V = \frac{4 \times 5.832}{3} = \frac{23.328}{3} \approx 7.776
\]
Thus, the volume in terms of \( \pi \) is:
\[
V \approx 7.776 \pi \text{ yds}^3
\]
Rounding to the nearest hundredth, we have:
\[
7.78 \pi \text{ yds}^3
\]
So the answer is:
**7.78π yds³**
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere.
Given the radius \( r = 1.8 \) yards, we can substitute this value into the formula:
\[
V = \frac{4}{3} \pi (1.8)^3
\]
First, we need to calculate \( (1.8)^3 \):
\[
(1.8)^3 = 1.8 \times 1.8 \times 1.8 = 5.832
\]
Now, substitute this value back into the volume formula:
\[
V = \frac{4}{3} \pi (5.832)
\]
Now, multiply \( 5.832 \) by \( \frac{4}{3} \):
\[
V = \frac{4 \times 5.832}{3} = \frac{23.328}{3} \approx 7.776
\]
Thus, the volume in terms of \( \pi \) is:
\[
V \approx 7.776 \pi \text{ yds}^3
\]
Rounding to the nearest hundredth, we have:
\[
7.78 \pi \text{ yds}^3
\]
So the answer is:
**7.78π yds³**