The surface area of a sphere is 7.847 ft.? What is the radius of this sphere? (1 point)
The surface area of a sphere is given by the formula A = 4πr^2, where A is the surface area and r is the radius.
We can rearrange the formula to solve for r:
r = √(A / (4π))
Substituting the given surface area A = 7.847 ft^2 into the formula:
r = √(7.847 / (4π))
Using a calculator to evaluate the expression:
r ≈ 0.9935 ft
Therefore, the radius of the sphere is approximately 0.9935 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)
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Substituting the given radius r = 3 cm into the formula:
V = (4/3)π(3^3)
= (4/3)(3.14)(27)
≈ 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)
• sphere - cone = cylinder
• sphere = cylinder + cone
• 3 cones = 1 cylinder
• 1 cylinder = 2 cones + 1 sphere
The relationship between the volume formulas for the sphere, cylinder, and cone is as follows:
sphere = cylinder + cone
This is the correct answer.
are you sure
My apologies for the mistake. The correct relationship between the volume formulas for the sphere, cylinder, and cone is:
1 cone = 1/3 cylinder + 1/3 sphere
So, the correct answer is: 1 cone = 1/3 cylinder + 1/3 sphere
The volume of a sphere is 48 m
. 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)
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 m^3, we can set up an equation:
(4/3)πr^3 = 48
To find the radius, we can rearrange the equation and solve for r:
r^3 = (3/4)(48/π)
r^3 = 36/π
r = ∛(36/π)
Once we find the radius, we can determine the height of the cylinder, which is equal to the diameter of the sphere:
h = 2r
Now we can calculate the volume of the cylinder using the formula V = πr^2h:
V = π(r^2)(2r)
V = 2πr^3
Substituting the value of r we found earlier:
V = 2π(∛(36/π))^3
Using a calculator to evaluate the expression:
V ≈ 2π(2.6207)^3
V ≈ 63.327 m^3
Therefore, the volume of the cylinder is approximately 63.327 m^3.