Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To find the volume of a sphere given its diameter, follow these steps:
1. Determine the Radius: The diameter of the sphere is given as [tex]\( 14 \)[/tex] feet. The radius of a sphere is half its diameter. Hence,
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{feet} \][/tex]
2. Write the Formula for the Volume of a Sphere: The formula to find the volume [tex]\( V \)[/tex] of a sphere is:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
3. Substitute the Radius into the Volume Formula: Now, substitute the value of the radius [tex]\( r = 7 \)[/tex] feet into the formula:
[tex]\[ V = \frac{4}{3} \pi (7)^3 \][/tex]
4. Calculate [tex]\( 7^3 \)[/tex]: First, find the cube of the radius:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
5. Plug the Cubed Radius Back into the Volume Formula:
[tex]\[ V = \frac{4}{3} \pi (343) \][/tex]
6. Simplified Equation: This gives us the equation for the volume of the sphere:
[tex]\[ V = \frac{4}{3} \pi (7)^3 \][/tex]
Therefore, the correct equation that finds the volume of the sphere is:
[tex]\[ \boxed{V = \frac{4}{3} \pi (7)^3} \][/tex]
1. Determine the Radius: The diameter of the sphere is given as [tex]\( 14 \)[/tex] feet. The radius of a sphere is half its diameter. Hence,
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{feet} \][/tex]
2. Write the Formula for the Volume of a Sphere: The formula to find the volume [tex]\( V \)[/tex] of a sphere is:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
3. Substitute the Radius into the Volume Formula: Now, substitute the value of the radius [tex]\( r = 7 \)[/tex] feet into the formula:
[tex]\[ V = \frac{4}{3} \pi (7)^3 \][/tex]
4. Calculate [tex]\( 7^3 \)[/tex]: First, find the cube of the radius:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
5. Plug the Cubed Radius Back into the Volume Formula:
[tex]\[ V = \frac{4}{3} \pi (343) \][/tex]
6. Simplified Equation: This gives us the equation for the volume of the sphere:
[tex]\[ V = \frac{4}{3} \pi (7)^3 \][/tex]
Therefore, the correct equation that finds the volume of the sphere is:
[tex]\[ \boxed{V = \frac{4}{3} \pi (7)^3} \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.