Find the surface area of a hemisphere with a radius 10m. Leave your answer in terms of pi.(1 point)
Responses
500π m2
500 pi m squared
400π m2
400 pi m squared
300π m2
300 pi m squared
200π m2
9 answers
200 pi m squared
The surface area of a sphere is 7.84π ft.2 What is the radius of this sphere?(1 point)
To find the radius of the sphere, we need to use the formula for the surface area of a sphere:
Surface Area = 4πr^2
Given that the surface area is 7.84π ft^2, we can set up the equation:
7.84π = 4πr^2
Dividing both sides of the equation by 4π, we get:
r^2 = (7.84π)/(4π)
r^2 = 1.96
Taking the square root of both sides, we find:
r = √1.96
r ≈ 1.4
Therefore, the radius of the sphere is approximately 1.4 feet.
Surface Area = 4πr^2
Given that the surface area is 7.84π ft^2, we can set up the equation:
7.84π = 4πr^2
Dividing both sides of the equation by 4π, we get:
r^2 = (7.84π)/(4π)
r^2 = 1.96
Taking the square root of both sides, we find:
r = √1.96
r ≈ 1.4
Therefore, the radius of the sphere is approximately 1.4 feet.
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.(1 point)
To find the volume of the spherical scoop of ice cream, we can use the formula for the volume of a sphere:
Volume = (4/3)πr^3
Given that the radius is 3 cm and using the approximation of π as 3.14, we can calculate:
Volume = (4/3) * 3.14 * (3^3)
Volume ≈ 113.04 cm^3
Rounding to the nearest whole number, the scoop of ice cream contains approximately 113 cm^3 of ice cream.
Volume = (4/3)πr^3
Given that the radius is 3 cm and using the approximation of π as 3.14, we can calculate:
Volume = (4/3) * 3.14 * (3^3)
Volume ≈ 113.04 cm^3
Rounding to the nearest whole number, the scoop of ice cream contains approximately 113 cm^3 of ice cream.
Suppose a sphere, cylinder, and cone all share the same radius and the cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
Responses
sphere - cone = cylinder
sphere - cone = cylinder
1 cylinder = 2 cones + 1 sphere
1 cylinder = 2 cones + 1 sphere
3 cones = 1 cylinder
3 cones = 1 cylinder
sphere = cylinder + cone
Responses
sphere - cone = cylinder
sphere - cone = cylinder
1 cylinder = 2 cones + 1 sphere
1 cylinder = 2 cones + 1 sphere
3 cones = 1 cylinder
3 cones = 1 cylinder
sphere = cylinder + cone
The correct relationship between the volume formulas for the sphere, cylinder, and cone in this scenario is:
sphere = cylinder + cone
sphere = cylinder + cone
The volume of a sphere is 48 m3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)
To find the volume of the cylinder, we need to determine the radius and height of the cylinder.
Given that the radius of the cylinder is the same as the sphere, we know that the radius of the cylinder is r.
The height of the cylinder is equal to the sphere's diameter, which means it is twice the radius of the sphere. Therefore, the height of the cylinder is 2r.
The volume formula for a cylinder is: V = πr^2h
Substituting the values we have:
V = π * r^2 * 2r
V = 2πr^3
We are given that the volume of the sphere is 48 m^3. The volume of the sphere is given by:
V_sphere = (4/3)πr^3
Substituting the known values:
48 = (4/3)πr^3
To cancel out the (4/3)π, we can divide both sides of the equation by (4/3)π:
(3/4)*(48) = r^3
36 = r^3
Taking the cube root of both sides:
r = 3
Now we can substitute the value of r into the volume formula for the cylinder:
V = 2π * (2^3)
V = 2π * 8
V = 16π
Therefore, the volume of the cylinder is 16π m^3.
Given that the radius of the cylinder is the same as the sphere, we know that the radius of the cylinder is r.
The height of the cylinder is equal to the sphere's diameter, which means it is twice the radius of the sphere. Therefore, the height of the cylinder is 2r.
The volume formula for a cylinder is: V = πr^2h
Substituting the values we have:
V = π * r^2 * 2r
V = 2πr^3
We are given that the volume of the sphere is 48 m^3. The volume of the sphere is given by:
V_sphere = (4/3)πr^3
Substituting the known values:
48 = (4/3)πr^3
To cancel out the (4/3)π, we can divide both sides of the equation by (4/3)π:
(3/4)*(48) = r^3
36 = r^3
Taking the cube root of both sides:
r = 3
Now we can substitute the value of r into the volume formula for the cylinder:
V = 2π * (2^3)
V = 2π * 8
V = 16π
Therefore, the volume of the cylinder is 16π m^3.
1 answer