1. The volume of a sphere is 1,476 pi m^3. What is the surface area of the sphere to the nearest tenth?
A) 629.9 m^2
B) 672.4 m^2
c) 1,334.8 m^2
D) 1,973.5 m^2
Is the answer C?
yes
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr^2
To find the radius (r), we can use the formula for the volume of a sphere:
Volume = (4/3)πr^3
Given that the volume is 1,476π m^3, we can set up the equation:
1,476π = (4/3)πr^3
Divide both sides by (4/3)π:
1,476/((4/3)π) = r^3
Simplify the equation:
1,476/(4/3) = r^3
We can simplify further:
1,476/(4/3) = 1,476 * (3/4) = 1,107
Now, find the cube root of both sides to solve for r:
r = cube root of 1,107 ≈ 10.37
Now, substitute the radius into the surface area formula:
Surface Area = 4π(10.37)^2
Surface Area ≈ 4π(107.44)
Surface Area ≈ 427.68π
To find the surface area to the nearest tenth, we need to find the approximate value of π. Let's assume π ≈ 3.14.
Surface Area ≈ 427.68 * 3.14
Surface Area ≈ 1,341.63 m^2
The surface area of the sphere to the nearest tenth is approximately 1,341.6 m^2. Therefore, the answer is not C) 1,334.8 m^2.
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr²
First, we need to find the radius of the sphere. Since we are given the volume, we can use the formula for the volume of a sphere:
Volume = (4/3)πr³
Given that the volume is 1,476π m^3, we can set up the equation:
1,476π = (4/3)πr³
To solve for r, we divide both sides by (4/3)π:
1,476π / ((4/3)π) = r³
Simplifying:
1,476 / (4/3) = r³
(1,476 * 3) / 4 = r³
1,107 = r³
Take the cube root of both sides:
∛(1,107) = r
Therefore, r ≈ 10.96 meters (rounded to two decimal places).
Now that we have the radius (10.96 meters), we can substitute it into the formula for surface area:
Surface Area = 4π(10.96)²
Calculating this, the surface area is approximately 1,511.57 m² (rounded to two decimal places).
Since none of the given answer choices match exactly, it seems that there might be a mistake in one of the options or the calculation. Please double-check the options or recheck your calculations to find the correct answer.