Question

How do you find the volume of a sphere with a diameter of $ 2 $ inches?

Answer 1

Hint: First we will mention the formula for evaluating $ V = \dfrac{4}{3}\pi {r^3} $ .
Then we will evaluate all the required terms from the given question. Then we will apply the formula and evaluate the volume of the sphere.

Complete step-by-step answer:
We will mention the formula for the volume of a sphere.
 $ V = \dfrac{4}{3}\pi {r^3} $ .
Here, the value of $ \pi $ is a number that approximately equals $ 3.14\, $ and $ r $ is the radius of the sphere.
Remember that to use the formula, we need the value of the radius. Since the radius is half of the diameter, we can find the value of the radius by dividing $ 2 $ with $ 2 $ .
Hence, the radius will be,
 $
\Rightarrow r = \dfrac{d}{2} \\
\Rightarrow r = \dfrac{2}{2} \\
\Rightarrow r = 1 \;
  $
With the radius, $ r = 1 $ inches, we can calculate for the volume of the sphere.
 $
\Rightarrow V = \dfrac{4}{3}\pi {r^3} \\
\Rightarrow V = \dfrac{4}{3}(3.14) \times {(1)^3} \\
\Rightarrow V = \dfrac{4}{3}(3.14) \times (1) \times (1) \times (1) \\
\Rightarrow V = \dfrac{4}{3}(3.14){(1)^3} \\
\therefore V = 4.1762 \;
  $
Now, it is important to include the unit. Since, the radius is in inches. The volume will be in cubic inches. Therefore, the volume of the sphere is $ 4.1762\,i{n^3} $ .
So, the correct answer is “$ 4.1762\,i{n^3} $”.

Note: A sphere is a set of points in space that are at a given distance $ r $ from the centre. The volume of a $ 3 $ - dimensional solid is the amount of space it occupies. Volume is measured in cubic units.