write the formula for the following 3 - dimensional objects.
1) cylinder =
2) cone =
3) sphere =
4) what is the diameter?
5) what is the radius?
round the following number to the nearest.... 347.851
6) tenths
7) hundredths
find the volume of each figure. show all work and round to the nearest tenth!
8.
9.

Question

Accepted Answer

### 1) Cylinder Formula
# Explanation:
## Step1: Recall cylinder volume formula
The volume of a cylinder is given by the area of the base (a circle) multiplied by the height. The area of a circle is $ \pi r^2 $, so the volume $ V $ of a cylinder with radius $ r $ and height $ h $ is $ V=\pi r^{2}h $.
# Answer:
$ V = \pi r^2 h $ (where $ V $ is volume, $ r $ is radius, $ h $ is height)

### 2) Cone Formula
# Explanation:
## Step1: Recall cone volume formula
The volume of a cone is one - third of the volume of a cylinder with the same base and height. So, if the radius is $ r $ and height is $ h $, the volume $ V $ of a cone is $ V=\frac{1}{3}\pi r^{2}h $.
# Answer:
$ V=\frac{1}{3}\pi r^{2}h $ (where $ V $ is volume, $ r $ is radius, $ h $ is height)

### 3) Sphere Formula
# Explanation:
## Step1: Recall sphere volume formula
The volume $ V $ of a sphere with radius $ r $ is given by the formula $ V = \frac{4}{3}\pi r^{3} $.
# Answer:
$ V=\frac{4}{3}\pi r^{3} $ (where $ V $ is volume, $ r $ is radius)

### 4) Diameter Definition
# Brief Explanations:
The diameter of a circle (or a circular cross - section of a 3 - D object like a cylinder or cone) is a straight line passing through the center of the circle, and its length is twice the radius. Mathematically, if $ r $ is the radius, the diameter $ d=2r $.
# Answer:
The diameter ($ d $) of a circle is the distance across the circle passing through its center, and $ d = 2r $ (where $ r $ is the radius).

### 5) Radius Definition
# Brief Explanations:
The radius of a circle (or a circular cross - section of a 3 - D object) is the distance from the center of the circle to any point on the circle's circumference. Mathematically, if $ d $ is the diameter, the radius $ r=\frac{d}{2} $.
# Answer:
The radius ($ r $) of a circle is the distance from the center of the circle to a point on the circle's edge, and $ r=\frac{d}{2} $ (where $ d $ is the diameter).

### 6) Round 347.851 to the nearest tenths
# Explanation:
## Step1: Identify the tenths and hundredths place
In the number $ 347.851 $, the digit in the tenths place is $ 8 $ and the digit in the hundredths place is $ 5 $.
## Step2: Apply rounding rule
When rounding to the nearest tenths, we look at the digit in the hundredths place. If the digit in the hundredths place is $ 5 $ or greater, we round up the digit in the tenths place. Since $ 5\geq5 $, we add $ 1 $ to the tenths place digit. So $ 347.851\approx347.9 $.
# Answer:
$ 347.9 $

### 7) Round 347.851 to the nearest hundredths
# Explanation:
## Step1: Identify the hundredths and thousandths place
In the number $ 347.851 $, the digit in the hundredths place is $ 5 $ and the digit in the thousandths place is $ 1 $.
## Step2: Apply rounding rule
When rounding to the nearest hundredths, we look at the digit in the thousandths place. If the digit in the thousandths place is less than $ 5 $, we leave the digit in the hundredths place as it is. Since $ 1\lt5 $, $ 347.851\approx347.85 $.
# Answer:
$ 347.85 $

### 8) Volume of Cylinder
# Explanation:
## Step1: Recall cylinder volume formula
The volume $ V $ of a cylinder is given by $ V=\pi r^{2}h $, where $ r = 6.5\space cm $ and $ h=16\space cm $.
## Step2: Substitute the values
Substitute $ r = 6.5 $ and $ h = 16 $ into the formula: $ V=\pi\times(6.5)^{2}\times16 $.
First, calculate $ (6.5)^{2}=42.25 $. Then, $ V=\pi\times42.25\times16 $. $ 42.25\times16 = 676 $. So $ V = 676\pi\approx676\times3.1416\approx2123.72 \space cm^{3} $. Rounding to the nearest tenth, we get $ 2123.7\space cm^{3} $ (if we use $ \pi\approx3.14 $, $ 676\times3.14 = 2122.64\approx2122.6\space cm^{3} $, but using a more accurate value of $ \pi\approx3.1416 $ gives $ 2123.7\space cm^{3} $).
# Answer:
Approximately $ 2123.7\space cm^{3} $ (or $ 2122.6\space cm^{3} $ if $ \pi\approx3.14 $)

### 9) Volume of Cone
# Explanation:
## Step1: Recall cone volume formula
The volume $ V $ of a cone is given by $ V=\frac{1}{3}\pi r^{2}h $, where $ r = 3\space cm $ and $ h = 8\space cm $.
## Step2: Substitute the values
Substitute $ r = 3 $ and $ h = 8 $ into the formula: $ V=\frac{1}{3}\times\pi\times(3)^{2}\times8 $.
First, calculate $ (3)^{2}=9 $. Then, $ \frac{1}{3}\times9\times8=24 $. So $ V = 24\pi\approx24\times3.1416\approx75.4\space cm^{3} $ (when rounded to the nearest tenth).
# Answer:
Approximately $ 75.4\space cm^{3} $

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QUESTION IMAGE

Question

Explanation:

1) Cylinder Formula

Step1: Recall cylinder volume formula

Step1: Recall cone volume formula

Step1: Recall sphere volume formula

Answer:

2) Cone Formula