find the radius of a sphere withh the given property.
A.The number of square meters of a surface area equals the number of cubic meters of volume.
B. The ratio of surface area in square meters to volume in cubic meters is 1:5.
we want
4/3 pi r^3 = 4pi r^2
1/3 r = 1
r = 3
next,
4/3 pi r^3 = 5*4pi r^2
1/3 r = 5
r = 15
To find the radius of a sphere with the given properties, we can use the formulas for the surface area and volume of a sphere.
A. The number of square meters of surface area equals the number of cubic meters of volume.
For a sphere, the formula for surface area is: A = 4πr²
And the formula for volume is: V = (4/3)πr³
Since the number of square meters of surface area is equal to the number of cubic meters of volume, we can set these two formulas equal to each other:
4πr² = (4/3)πr³
To solve for r, we can simplify the equation:
4πr² = 4/3πr³
3 * 4πr² = 4πr³
12πr² = 4πr³
3r² = r³
Now, we divide both sides of the equation by r²:
3 = r
Therefore, the radius of the sphere in this case is 3 units.
B. The ratio of surface area to volume is 1:5.
Again, the formula for surface area is A = 4πr², and the formula for volume is V = (4/3)πr³.
Given the ratio of surface area to volume as 1:5, we can set up the following equation:
4πr² : (4/3)πr³ = 1 : 5
To simplify the equation, we can cancel out the common factors:
(4πr²) / (4/3)πr³ = 1/5
3 = r
Therefore, the radius of the sphere in this case is 3 units.
In both cases, the radius of the sphere is 3 units.