find the surface area of a grape fruit with a circumference of 14cm. round your answer to the nearest number
The formula to find the surface area of a sphere (like a grapefruit) is:
Surface area = 4πr^2
To use this formula, we first need to find the radius of the grapefruit. We know that the circumference (the distance around the outside) is 14cm. The formula to find the circumference of a sphere is:
Circumference = 2πr
We can rearrange this formula to solve for the radius:
r = Circumference ÷ 2π
r = 14cm ÷ 2π
r ≈ 2.23cm (rounded to two decimal places)
Now we can plug this radius into the formula for the surface area:
Surface area = 4π(2.23cm)^2
Surface area ≈ 62.40cm^2
Surface area ≈ 62cm^2 (rounded to the nearest whole number)
To find the surface area of a grapefruit, we need to know the diameter of the fruit. The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere. Since we only have the circumference, we need to find the diameter first.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Rearranging the formula, we have d = C/π.
Given that the circumference is 14 cm, we can calculate the diameter as follows:
d = 14 cm / π ≈ 4.46 cm
Now that we have the diameter (d ≈ 4.46 cm), we can find the radius (r) by dividing the diameter by 2:
r = d/2 ≈ 4.46 cm / 2 ≈ 2.23 cm
Finally, we can find the surface area (A) of the grapefruit using the formula 4πr^2:
A = 4π(2.23 cm)^2 ≈ 62.47 cm^2
Rounding the answer to the nearest whole number, we get the surface area of the grapefruit as approximately 62 cm^2.