Question

find the surface area of a hemisphere with a radius of 10 m leave your answer in terms of Pi.

300 Pi m^2
400 Pi m^2
500 Pi m^2
200 pi m^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The surface area of a hemisphere can be found using the formula:

Surface Area = 2πr²

where r is the radius of the hemisphere.

Given a radius of 10 m, we can substitute this value into the formula:

Surface Area = 2π(10)^2
Surface Area = 2π(100)
Surface Area = 200π m^2

Therefore, the surface area of the hemisphere is 200π m^2.

Answer 2

the surface area of a sphere is 7.84 PI ft ^2 What is the radius of the sphere ?

Answer 3

[AI-generated answer — Bot GPT 3.5]

The formula for the surface area of a sphere is:

Surface Area = 4πr²

Given that the surface area is 7.84π ft², we can set up the equation:

7.84π = 4πr²

To solve for the radius (r), we need to isolate it on one side of the equation.

Dividing both sides of the equation by 4π:

r² = (7.84π) / (4π)
r² = 1.96

Taking the square root of both sides:

r = √(1.96)
r ≈ 1.4 ft

Therefore, the radius of the sphere is approximately 1.4 ft.

Answer 4

How much ice cream is in a spherical scoop of ice cream with a radius of 3 cm? Use 3.14 as an approximation for pi. Round your answer to the nearest whole number.

Answer 5

[AI-generated answer — Bot GPT 3.5]

The volume of a sphere can be calculated using the formula:

Volume = (4/3) * π * r^3

Given a radius of 3 cm and approximating π as 3.14, we can substitute these values into the formula:

Volume = (4/3) * 3.14 * (3)^3
Volume ≈ (4/3) * 3.14 * 27
Volume ≈ 113.04 cm^3

Rounding the answer to the nearest whole number, the spherical scoop of ice cream contains approximately 113 cm^3 of ice cream.

Answer 6

The volume of a sphere is 48m^3 what is the volume of a cylinder if it's radius is the same ad the spheres and its height is equal to the spheres diameter

Answer 7

[AI-generated answer — Bot GPT 3.5]

The formula for the volume of a sphere is:

Volume = (4/3) * π * r^3

Given a volume of 48 m³, we can solve for the radius (r) of the sphere:

48 = (4/3) * π * r^3

To find the radius, we rearrange the equation to isolate r:

r^3 = (48 * 3) / (4 * π)
r^3 = 36 / π
r ≈ 3.02 m

Now that we know the radius of the sphere is approximately 3.02 m, we can calculate the radius of the cylinder since it is given to be the same as the sphere. The radius of the cylinder is 3.02 m.

Additionally, given that the height of the cylinder is equal to the sphere's diameter, we know that the height of the cylinder is twice the radius (2r).

Therefore, the height of the cylinder is:

Height = 2 * r = 2 * 3.02 m ≈ 6.04 m

Now we can use the formula for the volume of a cylinder to find the volume of the cylinder:

Volume = π * r^2 * h

Volume = π * (3.02)^2 * 6.04
Volume ≈ π * 9.1204 * 6.04
Volume ≈ 173.7 m³

Therefore, the volume of the cylinder is approximately 173.7 m³.