a sphere has a volume of 900 cubic inches. find its surface area to the nearest whole number
To find the surface area of a sphere, we use the formula:
SA = 4πr^2
where r is the radius of the sphere.
To solve for the radius, we use the formula for the volume of a sphere:
V = (4/3)πr^3
We know the volume of the sphere is 900 cubic inches, so we can set up an equation:
900 = (4/3)πr^3
Solving for r, we get:
r = 7.5 inches
Now we can find the surface area:
SA = 4π(7.5)^2
SA ≈ 706
Therefore, the surface area of the sphere is 706 square inches (to the nearest whole number).
To find the surface area of a sphere, you need to know its volume. However, you have provided the volume of the sphere, so we'll have to work in reverse.
The formula for the volume of a sphere is:
V = (4/3) * π * r³,
where V is the volume and r is the radius of the sphere.
Given that the volume V is 900 cubic inches, we can rearrange the formula to solve for the radius:
r = ((3 * V) / (4 * π))^(1/3).
Substituting the value of V = 900 into the equation:
r = ((3 * 900) / (4 * 3.14))^(1/3) ≈ 7.44 inches (rounded to two decimal places).
Now that we know the radius of the sphere is approximately 7.44 inches, we can find its surface area using the formula:
A = 4 * π * r².
Substituting the value of r = 7.44 into the equation:
A = 4 * 3.14 * (7.44)^2 ≈ 349 square inches (rounded to the nearest whole number).
Therefore, the surface area of the sphere is approximately 349 square inches.
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr^2,
where r is the radius of the sphere.
To find the radius, we need to know the volume of the sphere. The formula for the volume of a sphere is:
Volume = (4/3)πr^3.
Given that the volume of the sphere is 900 cubic inches, we can set up the equation:
900 = (4/3)πr^3.
To solve for r, we can rearrange the equation as follows:
r^3 = (3/4) * (900 / π).
Calculating (3/4) * (900 / π) gives us approximately 269.4932.
To find the cube root of 269.4932, we need a calculator or a software that can perform cubic root calculations. Taking the cube root gives us approximately 6.76.
Now that we have the radius, we can calculate the surface area of the sphere:
Surface Area = 4π * (6.76)^2.
Evaluating this expression gives us approximately 911.77 square inches.
Rounding this value to the nearest whole number, the surface area of the sphere is approximately 912 square inches.