A spherical balloon has a circumference of 19 cm. What is the approximate surface area of the balloon to the nearest square centimeter?
A. 115 cm^2
B. 460 cm^2
C. 361 cm^2
D. 1,134 cm^2
What is the volume of the sphere? Round the answer to the nearest cubic unit.
Radius: 18 cm
A. 3,054 cm^3
B. 339 cm^3
C. 763 cm^3
D. 9,160 cm^3
To find the radius of the balloon, we can use the formula for circumference: C = 2πr. Plugging in the given circumference, we get:
19 = 2πr
r ≈ 3.03 cm
Now we can use the formula for surface area of a sphere: S = 4πr^2. Plugging in the radius we just found, we get:
S ≈ 115 cm^2
Therefore, the answer is A. 115 cm^2.
To find the volume of the sphere, we can use the formula V = (4/3)πr^3. Plugging in the radius we found earlier, we get:
V ≈ 3,054 cm^3
Therefore, the answer is A. 3,054 cm^3 (rounded to the nearest cubic unit).
To find the surface area of a sphere, we use the formula:
Surface Area = 4πr²
Where r is the radius of the sphere.
In this case, the circumference is given as 19 cm, which is equal to the formula for circumference:
Circumference = 2πr
To find the radius, we can rearrange the formula:
r = Circumference / (2π)
Plugging in the given value for circumference:
r = 19 cm / (2π)
Using a calculator, we can calculate:
r ≈ 19 cm / (2 * 3.14)
r ≈ 3.03 cm
Now we can find the surface area using the formula:
Surface Area = 4π(3.03)^2
Using a calculator, we can calculate:
Surface Area ≈ 4 * 3.14 * (3.03)^2
Surface Area ≈ 4 * 3.14 * 9.1809
Surface Area ≈ 115.6928 cm^2
Rounding to the nearest square centimeter, the approximate surface area of the balloon is 116 cm^2.
Therefore, the correct answer is A. 115 cm^2.
To find the volume of a sphere, we use the formula:
Volume = (4/3)πr³
Given that the radius is 18 cm:
Volume = (4/3)π(18)^3
Using a calculator, we can calculate:
Volume ≈ (4/3) * 3.14 * (18)^3
Volume ≈ 4.19 * 3.14 * 5832
Volume ≈ 77090.24 cm^3
Rounding to the nearest cubic unit, the approximate volume of the sphere is 77090 cm^3.
Therefore, the correct answer is D. 9,160 cm^3.
To find the approximate surface area of the balloon, you can use the formula for the surface area of a sphere. The formula is A = 4πr^2, where A represents the surface area and r represents the radius of the sphere.
Given that the circumference of the balloon is 19 cm, you can use the formula for the circumference of a sphere, which is C = 2πr, where C represents the circumference and r represents the radius.
From the equation C = 2πr, you can solve for r by rearranging the equation as r = C / (2π).
Plugging in the given circumference, we have r = 19 cm / (2π) ≈ 3 cm (rounded to the nearest whole number).
Now that we have the radius, we can calculate the surface area using the formula A = 4πr^2:
A = 4π(3 cm)^2
A = 4π(9 cm^2)
A ≈ 113.1 cm^2
Since we need to round the answer to the nearest square centimeter, the approximate surface area of the balloon is 113 cm^2.
Therefore, the answer to the question is not listed among the options.