cone-shaped container on a farm is used for storing animal feed. The container has a radius of 4 feet and a height of 12 feet. What volume of feed, in cubic feet, can the container store? Round your answer to the nearest hundredth. Use 3.14 for π .(1 point)
GIVE AN CORRECT ANSWER
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Given that the radius is 4 feet and the height is 12 feet, we can substitute these values into the formula:
V = (1/3)(3.14)(4²)(12)
V ≈ (1/3)(3.14)(16)(12)
V ≈ (0.3333)(3.14)(16)(12)
V ≈ 200.96
Therefore, the container can store approximately 200.96 cubic feet of feed.
The surface area of a sphere is 7.84π ft.2 What is the radius of this sphere
The surface area of a sphere is given by the formula A = 4πr², where A is the surface area and r is the radius. Given that the surface area is 7.84π ft², we can substitute this value into the formula:
7.84π = 4πr²
Dividing both sides of the equation by 4π, we get:
r² = 7.84/4
r² = 1.96
Taking the square root of both sides, we find:
r ≈ √1.96
r ≈ 1.4
Therefore, the radius of this 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)
The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius. Given that the radius is 3 cm, we can substitute this value into the formula:
V = (4/3)(3.14)(3³)
V = (4/3)(3.14)(27)
V = (1.3333)(3.14)(27)
V = 113.04
Therefore, the spherical scoop of ice cream has approximately 113 cm³ 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)
The relationship between the volume formulas for the sphere, cylinder, and cone with the same radius is as follows:
The volume of a sphere is given by V = (4/3)πr³.
The volume of a cylinder is given by V = πr²h.
The volume of a cone is given by V = (1/3)πr²h.
Since the cylinder and cone share the same height, which is twice the radius, the volume formulas for the cylinder and cone can be written in terms of the same variable. Let's call the height of the cylinder and cone "h".
Therefore, the volume of the cylinder can be written as V_cylinder = πr²h, and the volume of the cone can be written as V_cone = (1/3)πr²h.
In comparison, the volume of the sphere is different from the volume formulas of the cylinder and cone. Therefore, the true statement about the relationship between the volume formulas for the sphere, cylinder, and cone is that the volume formula for the sphere is not the same as the volume formulas for the cylinder and cone.
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 =cylinder +cone
1 cylinder=2cones + 1 sphere
sphere-cone= cylinder
3 cones =1 cylinder
The correct statement about the relationship between the volume formulas for the sphere, cylinder, and cone is:
1 cylinder = 3 cones