A cone shaped container holds rice for four people. The container has a radius of 4 inches and a height of 12 inches. What is the volume of rice that can fit in the container? include both of pi (pi = 3.14 or pi = π).
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r^2 * h
Where r is the radius of the base of the cone and h is the height of the cone.
In this case, we have a cone with a radius of 4 inches and a height of 12 inches. Plugging these values into the formula, we get:
Volume = (1/3) * 3.14 * 4^2 * 12
Simplifying this expression, we have:
Volume = (1/3) * 3.14 * 16 * 12
Volume = 67.52 * 12
Volume = 810.24 cubic inches.
Therefore, the volume of rice that can fit in the container is 810.24 cubic inches.
ok, now in terms of pi
The volume of a cone in terms of π can be calculated using the formula:
Volume = (1/3) * π * r^2 * h
Where r is the radius of the base of the cone and h is the height of the cone.
In this case, we have a cone with a radius of 4 inches and a height of 12 inches. Plugging these values into the formula, we get:
Volume = (1/3) * π * 4^2 * 12
Simplifying this expression, we have:
Volume = (1/3) * π * 16 * 12
Volume = (1/3) * 16π * 12
Volume = (16π/3) * 12
Volume = (64π) * 4
Volume = 256π cubic inches.
Therefore, the volume of rice that can fit in the container is 256π cubic inches.
What does the diameter of a sphere represent? What do you know about the diameter?
The diameter of a sphere represents the longest straight-line distance between two points on the surface of the sphere, passing through the center. It can be thought of as the length of a line segment passing through the center and terminating at two points on the sphere's surface.
The diameter of a sphere is always twice the length of its radius. In other words, if we denote the diameter as "d" and the radius as "r," then the relationship between them is given by:
d = 2r
Knowing the diameter of a sphere allows us to easily calculate its radius and vice versa. Additionally, various properties such as the surface area and volume of the sphere can be determined based on the diameter or radius.
10) Find the surface area of a hemisphere (half of a sphere) with a radius of 6. Leave in terms of pi.
To find the surface area of a hemisphere with a radius of 6, we need to calculate the curved surface area.
The curved surface area of a hemisphere is given by the formula:
Surface Area = 2πr^2
where r is the radius of the hemisphere.
Plugging in the radius value of 6 into the formula, we get:
Surface Area = 2π(6)^2
Surface Area = 2π(36)
Surface Area = 72π
Therefore, the surface area of the hemisphere is 72π square units.
The surface area of a sphere is 6.8π. What is the radius of the sphere? Hint: what is the formula for surface area of a sphere?
The formula for the surface area of a sphere is:
Surface Area = 4πr^2
where r is the radius of the sphere.
In our case, we are given that the surface area of the sphere is 6.8π. Plugging this value into the formula, we have:
6.8π = 4πr^2
To isolate the radius, we'll divide both sides of the equation by 4π:
(6.8π) / (4π) = r^2
Now, simplifying the expression on the left side, we get:
1.7 = r^2
To find the radius, we take the square root of both sides:
√(1.7) = √(r^2)
r = √(1.7)
Therefore, the radius of the sphere is approximately √(1.7).