#1: A ball has a radius of 1 foot. What is the surface area of the ball?
A. 2 pi ft^2
B. 4 pi ft^2
C. 6 pi ft^2
D. 8 pi ft^2
#2: What is the approximate surface area of the sphere if the sphere has a measurement of 27 cm?
A. 247,000 cm^2
B. 9,160 cm^2
C. 36,600 cm^2
D. 339 cm^2
#1 i think is c.
#2 i think is b.
#1: A = 4πr^2 = 4π*1^2 = 4π
#2: correct, if the radius is 27cm.
To find the surface area of a sphere, we use the formula:
Surface Area = 4πr^2
where π is a constant (approximately 3.14) and r is the radius of the sphere.
For question #1, the radius of the ball is given as 1 foot.
Substituting that into the formula:
Surface Area = 4π(1^2) = 4π square feet.
So, the correct answer would be B: 4 pi ft^2.
For question #2, the measurement given is the diameter of the sphere, not the radius. To find the radius, we divide the diameter by 2.
Radius = 27 cm / 2 = 13.5 cm.
Now, let's substitute the radius into the formula:
Surface Area = 4π(13.5^2) = 4π(182.25) = 729π cm^2.
Since the answer choices are not in terms of π, we need to approximate this value.
Using the approximation π ≈ 3.14, we can calculate:
Surface Area ≈ 729 * 3.14 ≈ 2,289.06 cm^2.
So, the approximate surface area of the sphere is around 2,289.06 cm^2. Comparing this value to the answer choices, the closest option is A: 2,47,000 cm^2.