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.
The correct answer is:
Dimensions of the cube box should be approximately 4.506 in. × 4.506 in. × 4.506 in.
Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2 inches. Use 3.14 as an approximation for pi and round your answer to the nearest hundredth, if necessary. (1 point)
The formula for the volume of a sphere is given by:
Volume = (4/3)πr^3
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:
Volume = (4/3)π(4.6 inches)^3
Calculating the cube of the radius first:
(4.6 inches)^3 = 97.336 cubic inches
Now we can substitute this back into the formula:
Volume = (4/3)π(97.336 cubic inches)
Calculating the product:
Volume ≈ (4/3)π * 97.336 cubic inches
Using 3.14 as an approximation for π:
Volume ≈ (4/3) * 3.14 * 97.336 cubic inches
Volume ≈ 4.1888 * 97.336 cubic inches
Volume ≈ 407.008 cubic inches
Rounded to the nearest hundredth:
Volume ≈ 407.01 cubic inches
• 407.51 in.3
O 3,260.11 in.3
O 1, 222.54 in.3
O 115.55 in.3
The correct answer is:
Approximately 407.01 in.3
Find the volume of a sphere with a radius of 1.8 yards. Leave your answer in terms of pi. Round your answer to the nearest hundredth, if necessary.
The formula for the volume of a sphere is given by:
Volume = (4/3)πr^3
where r is the radius of the sphere.
In this case, the sphere has a radius of 1.8 yards.
Now we can substitute this value into the formula:
Volume = (4/3)π(1.8 yards)^3
Calculating the cube of the radius:
(1.8 yards)^3 = 5.832 cubic yards
Now we can substitute this back into the formula:
Volume = (4/3)π(5.832 cubic yards)
Calculating the product:
Volume ≈ (4/3)π * 5.832 cubic yards
The answer for volume of the sphere with a radius of 1.8 yards in terms of pi is:
Volume ≈ 7.744π cubic yards
Rounded to the nearest hundredth:
Volume ≈ 7.74π cubic yards
Use the formula for the volume of a sphere to solve the following problem.
How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth.
The formula for the volume of a sphere is given by:
Volume = (4/3)πr^3
where r is the radius of the sphere.
In this case, the basketball has a diameter of 9 inches, so the radius (r) is half of the diameter:
r = 9 inches / 2 = 4.5 inches
Now we can substitute this value into the formula:
Volume = (4/3)π(4.5 inches)^3
Calculating the cube of the radius first:
(4.5 inches)^3 = 91.125 cubic inches
Now we can substitute this back into the formula:
Volume = (4/3)π(91.125 cubic inches)
Calculating the product:
Volume ≈ (4/3)π * 91.125 cubic inches
Using 3.14 as an approximation for π:
Volume ≈ (4/3) * 3.14 * 91.125 cubic inches
Volume ≈ 4.1888 * 91.125 cubic inches
Volume ≈ 381.924 cubic inches
Rounded to the nearest tenth:
Volume ≈ 381.9 cubic inches
Therefore, approximately 381.9 cubic inches of air is needed to fill the basketball.
The volume of a container measures 4, 000 mmm^3 and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 as an approximation for pi How much space in the box is unused? Round your answer to the nearest tenth. (1 point)
The volume of the container is given as 4,000 mm^3.
To find the volume occupied by the 50 marbles, we need to calculate the volume of a single marble and then multiply it by the number of marbles.
The formula for the volume of a sphere is given by:
Volume = (4/3)πr^3
where r is the radius of the sphere.
In this case, the radius of each marble is given as 2 mm.
Now we can substitute this value into the formula:
Volume of a single marble = (4/3)π(2 mm)^3
Calculating the cube of the radius first:
(2 mm)^3 = 8 mm^3
Now we can substitute this back into the formula:
Volume of a single marble = (4/3)π(8 mm^3)
Calculating the product:
Volume of a single marble = (4/3)π * 8 mm^3
Volume of a single marble = 33.51 mm^3 (rounded to the nearest hundredth)
Now we can calculate the volume occupied by all 50 marbles:
Total volume occupied by the marbles = 50 * 33.51 mm^3
Total volume occupied by the marbles = 1675.5 mm^3 (rounded to the nearest tenth)
To find the unused space in the box, we subtract the volume occupied by the marbles from the total volume of the container:
Unused space = Volume of the container - Total volume occupied by the marbles
Unused space = 4000 mm^3 - 1675.5 mm^3
Unused space = 2324.5 mm^3 (rounded to the nearest tenth)
Therefore, approximately 2324.5 mm^3 of space in the box is unused.
Kairay created a sculpture by forming a hemisphere with a radius of 20 inches and then removing a hemisphere with a radius of 15 inches from it
Calculate the volume of his sculpture. Use 3 14 as an approximation for pi Round your answer to the nearest whole number
O 7,005 In.'
O 16, 747 in.' 0 9,682 tn."
O 10,363 t3
To calculate the volume of Kairay's sculpture, we need to find the volume of the hemisphere with a radius of 20 inches and then subtract the volume of the hemisphere with a radius of 15 inches.
The formula for the volume of a hemisphere is given by:
Volume = (2/3)πr^3
where r is the radius of the hemisphere.
For the larger hemisphere with a radius of 20 inches, we can calculate its volume as:
Volume of larger hemisphere = (2/3)π(20 inches)^3
Calculating the cube of the radius first:
(20 inches)^3 = 8000 cubic inches
Now we can substitute this back into the formula:
Volume of larger hemisphere = (2/3)π(8000 cubic inches)
Calculating the product:
Volume of larger hemisphere ≈ (2/3)π * 8000 cubic inches
Using 3.14 as an approximation for π:
Volume of larger hemisphere ≈ (2/3) * 3.14 * 8000 cubic inches
Volume of larger hemisphere ≈ 16,746.67 cubic inches
Now, let's calculate the volume of the smaller hemisphere with a radius of 15 inches:
Volume of smaller hemisphere = (2/3)π(15 inches)^3
Calculating the cube of the radius:
(15 inches)^3 = 3375 cubic inches
Now we can substitute this back into the formula:
Volume of smaller hemisphere = (2/3)π(3375 cubic inches)
Calculating the product:
Volume of smaller hemisphere ≈ (2/3)π * 3375 cubic inches
Using 3.14 as an approximation for π:
Volume of smaller hemisphere ≈ (2/3) * 3.14 * 3375 cubic inches
Volume of smaller hemisphere ≈ 7062.5 cubic inches
Finally, to find the volume of the sculpture, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere:
Volume of sculpture = Volume of larger hemisphere - Volume of smaller hemisphere
Volume of sculpture ≈ 16,746.67 cubic inches - 7062.5 cubic inches
Volume of sculpture ≈ 9673.17 cubic inches
Rounding to the nearest whole number:
Volume of sculpture ≈ 9,673 cubic inches
Therefore, the volume of Kairay's sculpture is approximately 9,673 cubic inches.
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 92 inches, so the radius (r) is half of the diameter:
r = 92 inches / 2 = 46 inches
Now we can substitute this value into the formula:
Surface Area = 4π(46 inches)^2
Calculating the square of the radius first:
(46 inches)^2 = 2116 square inches
Now we can substitute this back into the formula:
Surface Area = 4π(2116 square inches)
Calculating the product:
Surface Area ≈ 4π * 2116 square inches
Using 3.14 for π:
Surface Area ≈ 4 * 3.14 * 2116 square inches
Surface Area ≈ 26608.32 square inches
Rounded to the nearest hundredth:
Surface Area ≈ 26,608.32 square inches
The correct answer is:
Approximately 26,608.32 in^2