Find the approximate surface-area-to-volume ratio of the Moon. The radius of the Moon is 1,080 miles
Do it the same way I showed you for the last problem, Felix/Victoria.
360
To find the approximate surface-area-to-volume ratio of the Moon, we need to calculate the surface area and the volume of the Moon using its radius.
First, let's find the surface area of the Moon. The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
Using the given radius of the Moon, which is 1,080 miles, we can calculate the surface area as follows:
Surface Area = 4π × (1,080)^2 square miles
Calculating this, we get:
Surface Area ≈ 4π × 1,166,400 square miles
Surface Area ≈ 4.5994 × 10^6 square miles (rounded to four significant figures)
Next, let's find the volume of the Moon. The volume of a sphere is given by the formula:
Volume = (4/3)πr^3
Using the radius of the Moon, we can calculate the volume as follows:
Volume = (4/3)π × (1,080)^3 cubic miles
Calculating this, we get:
Volume ≈ (4/3)π × 1,311,120,000 cubic miles
Volume ≈ 5.532 × 10^11 cubic miles (rounded to four significant figures).
Now, let's find the ratio of the surface area to the volume:
Surface-area-to-volume ratio = Surface Area / Volume
Surface-area-to-volume ratio ≈ (4.5994 × 10^6) square miles / (5.532 × 10^11) cubic miles
Evaluating this, we get:
Surface-area-to-volume ratio ≈ 8.32 × 10^-6 square miles per cubic mile
Therefore, the approximate surface-area-to-volume ratio of the Moon is 8.32 × 10^-6 square miles per cubic mile.