A globe has a diameter of 24 inches. A smaller globe has a diameter of 18 inches.
What is the surface area to volume ratio of the smaller globe? Round to the nearest hundredth.
Well, let's get down to the math! The formula for the surface area of a sphere is 4πr², where r is the radius, and the formula for the volume is (4/3)πr³.
Since the diameter is given, we need to find the radius first. The radius of the smaller globe is half of the diameter, so it is 18/2 = 9 inches.
Now, let's calculate the surface area and volume:
Surface area = 4π(9)²
= 4π(81)
≈ 1018.35 square inches
Volume = (4/3)π(9)³
= (4/3)π(729)
≈ 3052.08 cubic inches
To find the surface area to volume ratio, we divide the surface area by the volume:
Surface area to volume ratio ≈ 1018.35 / 3052.08
≈ 0.334
So, the surface area to volume ratio of the smaller globe, rounded to the nearest hundredth, is approximately 0.33.
To find the surface area to volume ratio of the smaller globe, we need to calculate both the surface area and the volume of the globe.
To calculate the surface area of a sphere, we can use the formula: 4πr^2, where r is the radius of the sphere.
The radius of the smaller globe can be calculated by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 18 inches / 2 = 9 inches
Using this radius, we can calculate the surface area of the smaller globe:
Surface Area = 4πr^2 = 4π(9 inches)^2
Using the value for π (pi) as approximately 3.14159, we can substitute it into the equation and calculate the surface area:
Surface Area = 4π(9 inches)^2 ≈ 4 * 3.14159 * (9 inches)^2
Calculating this, we get:
Surface Area ≈ 1017.88 square inches
To calculate the volume of a sphere, we can use the formula: (4/3)πr^3.
Using the same radius (r = 9 inches), we can calculate the volume:
Volume = (4/3)πr^3 = (4/3)π(9 inches)^3
Calculating this, we get:
Volume ≈ 3053.63 cubic inches
Finally, we can calculate the surface area to volume ratio by dividing the surface area by the volume:
Surface Area to Volume Ratio = Surface Area / Volume
Substituting the values we have calculated, we get:
Surface Area to Volume Ratio ≈ 1017.88 square inches / 3053.63 cubic inches
Calculating this, we find:
Surface Area to Volume Ratio ≈ 0.33
To round this to the nearest hundredth, we round up because the next digit is 3 (greater than or equal to 5).
Therefore, the surface area to volume ratio of the smaller globe is approximately 0.33.