A hemispherical dome holds a volume of 486π..find the surface area (omit the area of the circle)?
I just need the formulas id use
To find the surface area of the hemispherical dome, you can use the formula:
Surface Area = 2πr^2
where r is the radius of the hemispherical dome.
However, before you can use the formula, you need to find the radius of the hemispherical dome using the volume information.
The volume of a hemisphere is given by the formula:
Volume = (2/3)πr^3
In this case, the volume of the hemispherical dome is given as 486π. So, you can set up the equation:
486π = (2/3)πr^3
To solve for r, divide both sides of the equation by (2/3)π:
486π / (2/3)π = r^3
After simplifying the right side:
486 / (2/3) = r^3
Finally, take the cube root of both sides to solve for r:
r = ∛(486 / (2/3))
Once you have the radius, you can substitute it into the surface area formula to find the surface area of the dome. Remember to omit the area of the circular base.
I hope this helps! Let me know if you have any further questions.
To find the surface area of a hemispherical dome, you can use the formulas for the surface area of a sphere and subtract the area of the circular base.
Here are the formulas you would use:
1. The formula for the surface area of a sphere is given by: A = 4πr^2, where A is the surface area and r is the radius of the sphere.
2. The area of the circular base is given by: A_base = πr^2, where A_base is the area of the circular base and r is the radius of the sphere.
Since a hemispherical dome is half of a sphere, you would use half the surface area formula for the sphere and subtract the area of the circular base.
Here's how you can calculate the surface area (omit the area of the circle):
1. Solve the equation for volume:
V = (2/3)πr^3 = 486π
2. Rearrange the equation to find the radius:
r^3 = (3/2) * 486
r^3 = 729
r = ∛729 = 9
3. Calculate the surface area using the formulas:
A = (1/2) * 4πr^2 - πr^2
A = 2πr^2 - πr^2
A = πr^2
A = π * (9)^2 = 81π
Therefore, the surface area of the hemispherical dome (omitting the area of the circle) is 81π.
volume = (1/2) (4/3) pi r^3 = (2/3)pi r^3
so
486 pi = (2/3) pi r^3
so
r^3 = (3/2)(486) = 729
area of half of hemisphere = (1/2) 4 pi r^2
= 2 pi (729)^(2/3)
= 162 pi
Volume of a sphere
=4πr³/3
Volume of hemisphere is half of the above.