The volume of a sphere is 2,098pim^3 what is the surface area to the nearest tenth
v = 4/3 pi r^3
a = 4pi*r^2
a = 4pi(3v/4)^(2/3) = 4pi(3*2098/4)^(2/3) = 1700.0
The 1700 matches my answer so is that the one I use
To find the surface area of a sphere, we can use the following formula:
Surface Area = 4πr^2
where "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the sphere.
Given the volume of the sphere, we can find the radius by rearranging the volume formula:
Volume = (4/3)πr^3
Given that the volume is 2,098π cubic units, we can rewrite the equation as:
2,098π = (4/3)πr^3
Now, let's solve for "r":
(4/3)πr^3 = 2,098π
Dividing both sides of the equation by (4/3)π:
r^3 = (2,098π * 3) / 4π
Simplifying further:
r^3 = 3 * 2,098 / 4
r^3 = 3 * 524.5
r^3 = 1,573.5
To find the value of "r," we need to take the cube root of 1,573.5:
r ≈ ∛1,573.5
Using a calculator, the approximate value of "r" is found to be 12.61. (Note: Keep all decimal places in your calculator until the end result for more accurate calculations.)
Now that we have the radius, we can substitute it into the formula for the surface area of a sphere:
Surface Area = 4πr^2
Surface Area ≈ 4 * π * (12.61)^2
Using a calculator, the approximate surface area is found to be 795.8 square units.
Rounding to the nearest tenth, the surface area of the sphere is approximately 795.8 square units.
Well, aren't you a curious little cookie! If the volume of a sphere is 2,098πm^3, then we can use the formula for the volume of a sphere (V = 4/3πr^3) to find its radius (r).
First, let's divide both sides of the equation by π to isolate the radius:
2,098π/π = (4/3πr^3)/π
2,098 = 4/3r^3
Next, we can multiply both sides by 3/4 to get rid of the fraction:
2,098 × 3/4 = r^3
1,573.5 = r^3
Now, we can find the cube root of both sides to get the radius:
r = ∛1,573.5 ≈ 12.6m
Phew! Now that we have the radius, we can use the formula for the surface area of a sphere (A = 4πr^2) to find the surface area of our spherical friend.
A = 4π(12.6)^2 ≈ 2,005.3m^2
So, the surface area of the sphere is approximately 2,005.3 square meters.
oops - lost a pi in the division
a = 4pi(3v/4pi)^(2/3) = 4pi(3*2098/4pi)^(2/3) = 792.5