Respuesta :
Formula for volume of sphere is:
[tex]V= \frac{4}{3} * r^{3} * \pi [/tex]
Now we insert
r=50000au
[tex]V= \frac{4}{3} * (50000au)^{3} * \pi \\ \\ V=523598775598298.87307710723054658 au^{3} \\ \\ V=5.2* 10^{14} au^{3}[/tex]
[tex]V= \frac{4}{3} * r^{3} * \pi [/tex]
Now we insert
r=50000au
[tex]V= \frac{4}{3} * (50000au)^{3} * \pi \\ \\ V=523598775598298.87307710723054658 au^{3} \\ \\ V=5.2* 10^{14} au^{3}[/tex]
The volume of the oort cloud that is in the shape of sphere is [tex]\boxed{Volume = 5.2 \times {{10}^{14}}a{u^3}}.[/tex]
Further explanation:
The volume of the sphere is [tex]\boxed{V=\frac{4}{3}\left({\pi {r^3}}\right)}.[/tex]
Here, V is the volume and r is the radius of the sphere.
The surface area of the sphere is [tex]\boxed{S = 4\pi {r^2}}.[/tex]
Given:
The radius of the oort cloud is [tex]r = 50000{\text{ au}}.[/tex]
Explanation:
The radius of the sphere is [tex]r = 50000{\text{ au}}.[/tex]
The volume of the oort cloud can be calculated as follows,
[tex]\boxed{Volume=\frac{4}{3}\times\pi \times{{\left(r\right)}^3}}[/tex]
Substitute [tex]\dfrac{{22}}{7}[/tex] for [tex]\pi, 50000[/tex] for r in above equation to obtain the volume of oort cloud.
[tex]\begin{aligned}Volume &= \frac{4}{3} \times \frac{{22}}{7} \times {\left( {50000} \right)^3}\\&=\frac{{88}}{{21}} \times 125\times {\left( {{{10}^4}} \right)^3}\\&= 523.8 \times {10^{12}}\\&= 5.238 \times {10^{14}}\\\end{aligned}[/tex]
Hence, the volume of the oort cloud that is in the shape of sphere is [tex]\boxed{Volume=5.2\times {{10}^{14}}a{u^3}}.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Mensuration
Keywords: Oort cloud, total volume, area, whole sphere, cubic, volume of the sphere, radius of the oort, diameter.
