a sphere has a volume of 12,348pi cubic inches. Find the surface area of the sphere.
(4/3)πr^3 = 12348π
r^3 = 9261
r = cuberoot(9261) = 21
SA = 4πr^2 = 4π(441) = 1764π square inches
Oh, I love a good math problem! To find the surface area of a sphere, we can use the formula: Surface Area = 4πr², where r is the radius of the sphere.
First, let's find the radius. We know that the volume of the sphere is 12,348π cubic inches. The formula for the volume of a sphere is: Volume = (4/3)πr³.
So, we can set up the equation: 12,348π = (4/3)πr³.
Dividing both sides by π, we get: 12,348 = (4/3)r³.
Now, let's solve for the radius. Taking the cube root on both sides, we have: r³ = (3/4)(12,348) = 9,261.
Taking the cube root again, we get: r ≈ 21.82.
Now that we have the radius, we can find the surface area. Plugging the radius into the formula Surface Area = 4πr², we get:
Surface Area = 4π(21.82)² ≈ 5,966.01 square inches.
So, the surface area of the sphere is approximately 5,966.01 square inches. Voila!
By the way, did you know that spheres make great party decorations? They're always rolling with the good times!
To find the surface area of a sphere, you can use the formula:
Surface Area = 4πr^2
Where r is the radius of the sphere.
In this case, we are given the volume of the sphere, which can be related to the radius of the sphere using the formula:
Volume = (4/3)πr^3
We can rearrange this formula to solve for the radius:
r^3 = (3/4) * (Volume / π)
r = cube root of [(3/4) * (Volume / π)]
Let's substitute the given volume into the formula and solve for the radius:
r = cube root of [(3/4) * (12348π / π)]
r = cube root of [(3/4) * 12348]
Calculating further:
r = cube root of (9261)
r ≈ 21
Now that we have the radius, we can find the surface area:
Surface Area = 4πr^2
Surface Area = 4π * 21^2
Surface Area = 4π * 441
Surface Area = 1764π
So, the surface area of the sphere is 1764π square inches.
To find the surface area of a sphere, you need to know its volume. However, in this case, we are given the volume of the sphere, but not its radius or diameter. Therefore, we'll work backward using the concept of volume and surface area.
The formula for the volume of a sphere is: V = (4/3)πr³, where V is the volume and r is the radius.
We are given: V = 12,348π cubic inches.
Let's set this equation up:
12,348π = (4/3)πr³
To find the radius, we'll rearrange the equation:
r³ = (3/4) * 12,348
r³ = 9,261
r ≈ 21.65 inches (rounded to two decimal places)
Now that we know the radius, we can find the surface area of the sphere using the formula: A = 4πr², where A is the surface area and r is the radius.
Substituting the value of r into the formula:
A = 4π * (21.65)²
A ≈ 5870.6 square inches (rounded to one decimal place)
Therefore, the surface area of the sphere is approximately 5870.6 square inches.