Find the surface area of a sphere that has a diameter of 32 inches. Use 3.14 for π.

Answer 1

First, we need to find the radius of the sphere. The radius is half of the diameter, so the radius is 32/2 = 16 inches.

The surface area of a sphere is given by the formula:
Surface Area = 4πr^2

Substitute the radius into the formula:
Surface Area = 4 * 3.14 * 16^2
Surface Area = 4 * 3.14 * 256
Surface Area = 3.14 * 1024
Surface Area ≈ 3218.56 square inches

Therefore, the surface area of the sphere with a diameter of 32 inches is approximately 3218.56 square inches.

Answer 2

How much larger (volume) is one large ball that has a radius if 21 inches than the total volume of 3 balls that each have a radius of 6 inches? Use 3.14 for π.

Answer 3

First, we need to calculate the volume of the larger ball with a radius of 21 inches.

The volume of a sphere is given by the formula:
Volume = (4/3) * π * r^3

For the larger ball:
Volume_large = (4/3) * 3.14 * 21^3
Volume_large = (4/3) * 3.14 * 9261
Volume_large = (4/3) * 3.14 * 9261
Volume_large = 4.19 * 9261
Volume_large ≈ 38817.59 cubic inches

Now, we need to calculate the total volume of three balls with a radius of 6 inches.

For each small ball:
Volume_small = (4/3) * 3.14 * 6^3
Volume_small = (4/3) * 3.14 * 216
Volume_small = 4.19 * 216
Volume_small ≈ 905.04 cubic inches

Total volume of the three small balls:
Total_volume_small = 3 * Volume_small
Total_volume_small = 3 * 905.04
Total_volume_small ≈ 2715.12 cubic inches

Now, we can compare the volume of the large ball to the total volume of the three small balls:
Difference = Volume_large - Total_volume_small
Difference = 38817.59 - 2715.12
Difference ≈ 36102.47 cubic inches

Therefore, the larger ball with a radius of 21 inches is approximately 36102.47 cubic inches larger in volume than the total volume of three balls, each with a radius of 6 inches.

Answer 4

Find the volume of a sphere that has a radius of 15 inches. Use 3.14 for π.

Answer 5

To find the volume of a sphere with a radius of 15 inches, we will use the formula for the volume of a sphere:

Volume = (4/3) * π * r^3

Given that the radius (r) is 15 inches and π is 3.14, we can calculate the volume:

Volume = (4/3) * 3.14 * 15^3
Volume = (4/3) * 3.14 * 3375
Volume = (4/3) * 3.14 * 3375
Volume = 4.19 * 3375
Volume ≈ 14137.5 cubic inches

Therefore, the volume of a sphere with a radius of 15 inches is approximately 14137.5 cubic inches.

Answer 6

Find the volume of a sphere that has a diameter of 100 inches. Use 3.14 for
.
The sphere’s volume is cubic inches.

Answer 7

To find the volume of a sphere with a diameter of 100 inches, we first need to find the radius. The radius is half of the diameter, so the radius is 100/2 = 50 inches.

Now, we can use the formula for the volume of a sphere:

Volume = (4/3) * π * r^3

Given that the radius (r) is 50 inches and π is 3.14, we can calculate the volume:

Volume = (4/3) * 3.14 * 50^3
Volume = (4/3) * 3.14 * 125000
Volume = (4/3) * 3.14 * 125000
Volume = 4.19 * 125000
Volume ≈ 523750 cubic inches

Therefore, the volume of a sphere with a diameter of 100 inches is approximately 523750 cubic inches.

Answer 8

How much larger is the calculation of the volume of a sphere’s whose radius is 45 inches if
is used instead of 3.14 ?
Round your answer to the nearest tenth.
The difference of using
rather than 3.14 is about cubic inches.

Answer 9

To calculate the volume of a sphere with a radius of 45 inches using π = 3.14159:

Volume = (4/3) * π * r^3
Volume = (4/3) * 3.14159 * 45^3
Volume = (4/3) * 3.14159 * 91125
Volume ≈ (4/3) * 3.14159 * 91125
Volume ≈ 4.18879 * 91125
Volume ≈ 381386.13 cubic inches

Now, let's calculate the volume of the same sphere with radius 45 inches using π = 3.14:

Volume = (4/3) * π * r^3
Volume = (4/3) * 3.14 * 45^3
Volume = (4/3) * 3.14 * 91125
Volume ≈ (4/3) * 3.14 * 91125
Volume ≈ 4.18667 * 91125
Volume ≈ 381172.60 cubic inches

The difference between the two calculations is approximately:
381386.13 - 381172.60 ≈ 213.53 cubic inches

Therefore, the difference of using π = 3.14159 rather than 3.14 is about 213.5 cubic inches.