Volume of Spheres Quick Check

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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

7.2π yds3
7.2 pi yds cubed

24.43π yds3
24.43 pi yds cubed

23.34π yds3
23.34 pi yds cubed

7.78π yds3
7.78 pi yds cubed

1 answer

To find the volume of a sphere, you use the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where \( r \) is the radius of the sphere. For a sphere with a radius of 1.8 yards, the calculation would be:

\[ V = \frac{4}{3} \pi (1.8)^3 \]

First, calculate \( (1.8)^3 \):

\[ (1.8)^3 = 1.8 \times 1.8 \times 1.8 = 5.832 \]

Then plug this value into the volume formula:

\[ V = \frac{4}{3} \pi (5.832) \]

Now calculate \( \frac{4}{3} \times 5.832 \):

\[ \frac{4}{3} \times 5.832 \approx 7.776 \]

So, the volume in terms of pi is:

\[ V \approx 7.776 \pi \text{ yds}^3 \]

Rounding \( 7.776 \) to the nearest hundredth gives you \( 7.78 \).

Thus, the volume of the sphere is:

\[ 7.78 \pi \text{ yds}^3 \]

From the options provided, the correct answer is:

7.78π yds³