Question

What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter?

Answer 1

`\rule{300}{1}`

`\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}`

What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?

`\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}`

We are asked to find the volume of a sphere, which we can find using the following formula:-

`\bold{V=(4)/(3) \pi r^3}`

Where:-

• V=volume
• π=pi (3.14…)
• r=radius

Provided information:-

• diameter (d)=32.5 m

What we need in order to find the volume:-

• radius

What we need in order to find the radius:-

• Since the radius is exactly one-half of the diameter, we divide the diameter by 2 in order to find the radius:-

`\bold{r=d/2}`

Replace d with 32.5:-

`\bold{r=32.5/2}`

Therefore, the sphere's radius is as follows:-

`\bold{r=16.25}` m

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Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-

`\bold{V=(4)/(3) \pi r^3}`

Replace r with 16.25:-

`\bold{V=(4)/(3) \pi (4291)}` Next, we replace π with 3.14:-

`\bold{V=(4)/(3) *3.14*4291}`

On simplification,

`\bold{V=(4)/(3) *13,473.74}`

On further simplification,

`\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}`

Good luck with your studies.

`\rule{300}{1}`

Answer 2

17,964.9 cubic meters

Explanation:

Hey there!

The formula for finding the area of a sphere is:

`V=(4/3)\pi r^3`

Where V is volume, and r is radius

The question already tells us that the diameter is 32.5m

*Remember, the diameter isn't the radius. It is the radius times two*

Now, we have to divide 32.5 by 2 to get the radius

32.5/2 is 16.25

Now we can plug this into the formula

16.25 cubed is 4291 after being rounded to the nearest tenth

Now we multiply 4291 by 3.14 (pi)

4291 x 3.14 is 13473.7 after being rounded to the nearest tenth

Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere

13473.7 x 4/3 is 17964.93333333...

Since it is asking us to round to the nearest tenth of a cubic meter;

The volume of the sphere will be 17,964.9 cubic meters