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.

Question

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

Answer 1

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

$$V=\frac{4}{3}\pi r^3$$

where $r$ is the radius of the sphere.

Given that the radius $r=1.8$ yards, we can substitute this value into the formula:

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

First, we calculate $(1.8{)}^3$:

$${1.8}^3=1.8\times 1.8\times 1.8=5.832$$

Now, substitute back into the volume formula:

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

Now calculate $\frac{4}{3}\times 5.832$:

$$\frac{4}{3}\times 5.832=\frac{4\times 5.832}{3}=\frac{23.328}{3}\approx 7.776$$

Thus, the volume is approximately:

$$V\approx 7.776\pi$$

So, the volume of the sphere in terms of pi is:

$$7.776\pi {\text{ yds}}^3$$

Rounding $7.776$ to the nearest hundredth gives $7.78$.

The final answer is:

$$\boxed{{\displaystyle 7.78\pi {\text{ yds}}^3}}$$