Question

asked Sep 27, 2023 127k views

1 Answer

Sherese · Answer 1 · 2023-10-03T13:31:11+0000

$\rule{300}{1} \\ \diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}$

What is the volume of a sphere with a diameter of 10m, rounded to the

nearest tenth of a cubic metre (m³)?

$\diamond\large\textsf{\textbf{\underline{Answer and How to solve:-}}}$

$\it{Volume\:of\:a\:sphere:-}$

$\longmapsto\sf{V=(4)/(3) \pi r^3}$

$\bold{\underline{Where:-}}$

Provided information:-

What we need in order to find the Volume:-

How to find the radius if we have the diameter?

Since the radius is exactly one-half of the diameter, we divide the diameter by 2:-

$\bold{r=d/2}$

Replace d with 10:-

$\bold{r=10/2}$

Therefore, the radius of the sphere is

$\bold{r=5}$

$\rule{300}{1}$

✓ Now we have all the required information in order to find the volume of the sphere.

✳︎Substitute 5 in lieu of r:-

$\bold{V=(4)/(3) \pi (5)^3}$

➪On simplification,

$\bold{V=(4)/(2) \pi (125)}$ ◈ Next, write the value of π (3.14…)

$\bold{V=(4)/(3)*3.14*125}$

On further simplification,

$\bold{V=(4)/(3) *392.5}$ Final Step:- Multiply the numbers.

$\bold{V=523.3\:m^3}$

The answer has been rounded to the nearest tenth (one place after the decimal point)

Therefore, we conclude that the volume of the sphere is

$\bold{V=523.3\:m^3}$

$\rule{301}{1}$