Use the formula for the surface area of a sphere to find the surface area of a basketball that has a diameter of 9.2 inches. Use 3.14 pi and round your answer to the nearest hundredth, if necessary.
A: 84.64 in^2
B: 66.44 in^2
C: 1,063.08 in^2
D: 265.77 in^2
The formula for the surface area of a sphere is A = 4πr^2, where r is the radius.
Since the diameter is given as 9.2 inches, we can find the radius by dividing the diameter by 2: 9.2 inches / 2 = 4.6 inches.
Now we can substitute the value of the radius into the equation: A = 4π(4.6 inches)^2.
Calculating this, we get A ≈ 265.77 square inches.
Rounding to the nearest hundredth, the surface area of the basketball is approximately 265.77 in^2.
Therefore, the correct answer is D: 265.77 in^2.
Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi
The formula for the surface area of a sphere is A = 4πr^2, where r is the radius.
Since the diameter is given as 30 inches, we can find the radius by dividing the diameter by 2: 30 inches / 2 = 15 inches.
Now we can substitute the value of the radius into the equation: A = 4π(15 inches)^2.
Simplifying further, we get A = 900π square inches.
Therefore, the surface area of the sphere is 900π square inches.
Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in^2 and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?
To find the dimensions of the cube box that will fit the spherical soap snugly, we need to determine the side length of the cube.
The surface area of a cube is given by the formula A = 6s^2, where s is the side length.
We are given that the surface area of the soap is 63.585 in^2. Let's set up the equation:
63.585 = 6s^2
Now, let's solve for s:
Divide both sides of the equation by 6:
63.585 / 6 = s^2
10.5975 = s^2
Take the square root of both sides to solve for s:
√10.5975 = s
s ≈ 3.26
Therefore, the side length of the cube box should be approximately 3.26 inches to fit the spherical soap snugly.
To find the surface area of a sphere, you can use the formula:
Surface Area = 4πr^2
where "r" is the radius of the sphere.
Given that the basketball has a diameter of 9.2 inches, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 9.2 inches / 2 = 4.6 inches
Now, substitute the radius into the formula:
Surface Area = 4π(4.6)^2
Calculate:
Surface Area = 4π(21.16)
Now, multiply 4π by 21.16:
Surface Area ≈ 84.64 square inches
Rounding to the nearest hundredth, the surface area of the basketball is approximately 84.64 square inches.
Therefore, the correct answer is A: 84.64 in^2.