Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches. Round your answer to the nearest hundredth. (1 point)
The diameter of a sphere is the longest distance on the sphere and is equal to twice the length of the radius. It passes through the center of the sphere and connects two points on its surface.
A 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 pi
The formula to find the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.
Substituting the given values, V = (1/3)(3.14)(4²)(12).
Calculating this expression, the volume of the cone is approximately 201.12 cubic feet.
The diameter of a sphere (1 point)
O is half the length of the radius.
O does not pass through the center of the sphere.
O is the longest distance on a sphere.
O is the distance from the center of the sphere to any point on the surface of the sphere
Find the surface area of a hemisphere with a radius 10m. Leave your answer in terms
of pi. (1 point)
O 200pi * m ^ 2
O 400pi * m ^ 2
500pi * m ^ 2
O 300pi * m ^ 2
The formula to find the surface area of a hemisphere is SA = 2πr², where r is the radius.
Substituting the given radius of 10m into the formula, SA = 2π(10)².
Calculating this expression, the surface area of the hemisphere is 400π m^2.
Therefore, the correct answer is 400pi * m^2.
The surface area of a sphere is 7.84pi*ft .^ 2 What is the radius of this sphere?
The formula to find the surface area of a sphere is SA = 4πr², where r is the radius.
Given that the surface area of the sphere is 7.84pi ft², we can set up the equation:
7.84π = 4πr².
Dividing both sides by 4π, we get:
r² = 1.96.
Taking the square root of both sides, we get:
r = √1.96.
Evaluating this expression, we find that the radius of the sphere is approximately 1.4 ft.
To find the volume of a cone, we can use the formula: V = (1/3) * π * r^2 * h
Given:
Radius (r) = 13 inches
Height (h) = 27 inches
Start by substituting the given values into the formula:
V = (1/3) * π * (13 inches)^2 * 27 inches
Next, calculate the value of (13 inches)^2:
r^2 = 13 inches * 13 inches = 169 inches^2
Now, substitute this value into the formula:
V = (1/3) * π * 169 inches^2 * 27 inches
To calculate the volume, we need to know the value of π (pi). π is a mathematical constant that is approximately equal to 3.14159. Let's use this value:
V = (1/3) * 3.14159 * 169 inches^2 * 27 inches
Now, simplify the expression:
V ≈ 14324.78 cubic inches
Rounding to the nearest hundredth, the volume of the cone is approximately 14324.78 cubic inches.
The formula to find the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.
Substituting the given values, V = (1/3)π(13²)(27).
Calculating this expression, the volume of the cone is approximately 19703.92 cubic inches.