Use the formula for the surface area of a sphere to find the surface aroa of a basketball that has a diameter of 92 inches. Use 3.14 pi and round your answer to the nearest hundredth, if necessary. (1 point)
O 66.44 in.^2
O 265.77 in.^2
O 1,063.08 in.^2
O 84.64 in.^2
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 (1 point)
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
where r is the radius of the sphere.
In this case, the basketball has a diameter of 9.2 inches, so the radius (r) is half of the diameter:
r = 9.2 inches / 2 = 4.6 inches
Now we can substitute this value into the formula:
Surface Area = 4π(4.6 inches)^2
Calculating the square of the radius first:
(4.6 inches)^2 = 21.16 square inches
Now we can substitute this back into the formula:
Surface Area = 4π(21.16 square inches)
Calculating the product:
Surface Area ≈ 4π * 21.16 square inches
Using 3.14 for π:
Surface Area ≈ 4 * 3.14 * 21.16 square inches
Surface Area ≈ 266.448 square inches
Rounded to the nearest hundredth:
Surface Area ≈ 266.45 square inches
O 66.44 in.^2
O 265.77 in.^2
O 1,063.08 in.^2
O 84.61 im.^2
The correct answer is:
Approximately 266.45 in^2
Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi. (1 point)
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
where r is the radius of the sphere.
In this case, the sphere has a diameter of 30 inches, so the radius (r) is half of the diameter:
r = 30 inches / 2 = 15 inches
Now we can substitute this value into the formula:
Surface Area = 4π(15 inches)^2
Calculating the square of the radius first:
(15 inches)^2 = 225 square inches
Now we can substitute this back into the formula:
Surface Area = 4π(225 square inches)
Simplifying:
Surface Area = 4π * 225 square inches
The answer for surface area of the sphere with diameter of 30 inches in terms of pi is:
Surface Area = 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? (1 point)
To find the dimensions of the cube box that will snugly fit the soap, we need to find the edge length of the cube. Since the soap has a spherical shape, the edge length of the cube should be equal to the diameter of the soap.
Given that the surface area of the soap is 63.585 in^2, and the formula for the surface area of a sphere is:
Surface Area = 4πr^2
where r is the radius of the sphere.
Let's solve for the radius:
63.585 in^2 = 4 * 3.14 * r^2
Dividing both sides by 4 * 3.14:
r^2 = 63.585 in^2 / (4 * 3.14)
Simplifying:
r^2 = 5.0796433125 in^2
Taking the square root of both sides to find the radius:
r ≈ √5.0796433125 in^2
r ≈ 2.253 in.
Since the radius of the sphere is equal to the edge length of the cube, the dimensions of the cube box that will snugly fit the soap are approximately:
Length = 2 * radius ≈ 2 * 2.253 in. ≈ 4.506 in.
Width = 2 * radius ≈ 2 * 2.253 in. ≈ 4.506 in.
Height = 2 * radius ≈ 2 * 2.253 in. ≈ 4.506 in.
So, the dimensions of the cube box should be approximately 4.506 inches in length, width, and height in order to snugly fit the soap.
O 4in. × 4in. × 4 in.
O 4.5 in. x 4.5 in. × 4.5 I.
O 2.25 in. x 2.25 In. x 2.25 in.
0 12 in. x 12 in. × 1.2 In.