can you explain in detail how to find the volume of a sphere?
To find the volume of a sphere, you can use the formula:
V = (4/3) * π * r^3
where:
V = volume of the sphere
π ≈ 3.14159
r = radius of the sphere
Here is a step-by-step guide on how to find the volume of a sphere:
1. Determine the radius of the sphere. The radius is the distance from the center of the sphere to any point on its surface.
2. Cube the radius. To do this, multiply the radius by itself three times. This will give you the value of r^3.
3. Multiply the cubed radius by (4/3) and π. This will give you the volume of the sphere. The value of π is approximately 3.14159.
4. Calculate the final answer. Round the volume to the nearest decimal if necessary.
For example, let's say the radius of the sphere is 5 cm:
V = (4/3) * π * 5^3
V = (4/3) * 3.14159 * 125
V = (1.33333333) * 125 * 3.14159
V ≈ 523.6 cubic cm
Therefore, the volume of the sphere with a radius of 5 cm is approximately 523.6 cubic cm.
im confused on the 3rd step, what are we doing with 4/3?
In the formula for the volume of a sphere, the (4/3) term is a constant that is necessary to convert the radius cubed value into the actual volume of the sphere. The value of 4/3 comes from the mathematical calculation of the volume of a sphere.
When you cube the radius of the sphere, you get the volume of a sphere formula which is V = (4/3) * π * r^3. The (4/3) term is used to account for the fact that a sphere is a three-dimensional shape and it requires a specific proportion to calculate its volume correctly.
In essence, multiplying the cubed radius by (4/3) converts the calculation into the correct volume of the sphere. This is why it's an important part of the formula for finding the volume of a sphere.
so were multiplying 125 by 3/4?
Yes, that's correct. In the formula for the volume of a sphere, you are multiplying the cubed radius by (4/3).
In the example provided with a radius of 5 cm:
V = (4/3) * π * 5^3
V = (4/3) * π * 125
Multiplying the cubed radius by (4/3), you get:
V = (4/3) * 125
V = (1.33333333) * 125
So, in this case, you are effectively multiplying the cubed radius (125) by 4/3 (or 1.33333333) to get the volume of the sphere.
Find the volume of a sphere with a diameter of 14 inches. Use 3.14 as an approximation for pi. Round to the nearest whole number.
please explain how to solve this? i got it wrong
To find the volume of a sphere with a diameter of 14 inches, you first need to find the radius. Remember, the radius is half of the diameter.
Given: Diameter = 14 inches
Radius = Diameter / 2 = 14 / 2 = 7 inches
Now, we will use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Given that π ≈ 3.14 and the radius (r) is 7 inches, substitute these values into the formula:
V = (4/3) * 3.14 * 7^3
V = (4/3) * 3.14 * 343
V = 4.187 * 343
V = 1436.021
After calculating, the volume of the sphere with a diameter of 14 inches is approximately 1436 cubic inches. Rounding to the nearest whole number, the volume is 1436 cubic inches.
can you please explain in more detail? im still confused
Of course! Let's break down the problem step by step:
1. Find the radius:
Given that the diameter of the sphere is 14 inches, we need to find the radius, which is half of the diameter.
Radius = Diameter / 2 = 14 / 2 = 7 inches
2. Plug the values into the formula for the volume of a sphere:
V = (4/3) * π * r^3
In this case, π is approximated as 3.14, and the radius (r) is 7 inches. Substitute these values into the formula:
V = (4/3) * 3.14 * 7^3
V = (4/3) * 3.14 * 343
V = 4.187 * 343
V = 1436.021
3. Round to the nearest whole number:
After calculating the volume as 1436.021 cubic inches, we need to round it to the nearest whole number. Since the decimal part is 0.021, we round up to the nearest whole number.
Therefore, the final volume of the sphere with a diameter of 14 inches is approximately 1436 cubic inches.
im confused on what exactly we do after we get to the step V = (4/3) * 3.14 * 343
After calculating V = (4/3) * 3.14 * 343, you need to perform the multiplication to find the volume of the sphere. Here's the detailed calculation:
1. Calculate the value of (4/3) * 3.14:
= (4/3) * 3.14
= 4.187
2. Multiply 4.187 by 343:
= 4.187 * 343
= 1436.021
Therefore, the volume of the sphere with a diameter of 14 inches is approximately 1436.021 cubic inches.
To round it to the nearest whole number, look at the decimal part (0.021). Since this is more than half, you round up the whole number. Therefore, the final volume is approximately 1436 cubic inches.