What is the solution for this?
The surface area of a sphere varies in direct proportion to the square of its radius. If a sphere of radius 6cm has a surface area of 452 square cm, find, to the nearest mm, the radius of a spherewith the surface area 1000 square cm.
36/452 = r^2/1000
r^2 = 36/.452
r = 8.9 cm
To find the radius of a sphere with a given surface area, we need to use the formula for the surface area of a sphere, which is:
Surface Area = 4πr^2
Where:
- Surface Area represents the surface area of the sphere
- π (Pi) is a mathematical constant approximately equal to 3.14159
- r represents the radius of the sphere
In this case, we have the surface area of the first sphere (452 square cm) and its radius (6 cm). We can plug these values into the formula to find a proportion between the surface area and the radius.
452 = 4π(6)^2
To find the radius of the sphere with a surface area of 1000 square cm, we need to rearrange the formula and solve for r:
Surface Area = 4πr^2
Divide both sides of the equation by 4π:
Surface Area / (4π) = r^2
Substitute the surface area into the equation:
1000 / (4π) = r^2
Now, we need to find the square root of both sides to isolate r:
√(1000 / (4π)) = √r^2
Simplify the equation:
r = √(1000 / (4π))
Calculating this using a calculator or a computer program, we find that the radius is approximately 7.98 cm.
Therefore, the radius of the sphere with a surface area of 1000 square cm, to the nearest mm, is 7.98 cm or 79.8 mm.