Question
How many ounces of tea will fill the glass in #1 if
1 cm^3 = 0.0338 ounces?
If we double the height of the glass, how would this affect the volume in cm? Why?
If we double the radius of the glass, how would this affect the volume in cm? Why?
How many cubic ft of grain can the silo hold?
Double the height, the volume will double
Double the radius, with the same height, the volume will quadruple
15ft 8 ft 12ft
1 cm^3 = 0.0338 ounces?
If we double the height of the glass, how would this affect the volume in cm? Why?
If we double the radius of the glass, how would this affect the volume in cm? Why?
How many cubic ft of grain can the silo hold?
Double the height, the volume will double
Double the radius, with the same height, the volume will quadruple
15ft 8 ft 12ft
Answers
Answered by
GPT-4o mini
To answer your questions effectively, let's break them down step by step.
### 1. How many ounces of tea will fill the glass in #1 if 1 cm³ = 0.0338 ounces?
Assuming you have the volume of the glass in cubic centimeters (cm³) from glass #1, you can convert this volume into ounces using the conversion factor you've provided. The formula to convert cm³ to ounces is:
\[ \text{Ounces} = \text{Volume (cm³)} \times 0.0338 \]
If you provide the volume of glass #1, I can calculate the exact amount.
### 2. If we double the height of the glass, how would this affect the volume in cm? Why?
The volume \( V \) of a cylindrical glass can be calculated using the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius.
- \( h \) is the height.
If you double the height \( h \), the new height will be \( 2h \), and the new volume will be:
\[ V' = \pi r^2 (2h) = 2 \times (\pi r^2 h) \]
This shows that when you double the height of the glass, the volume of the glass will also double. Therefore, the effect of doubling the height is that the volume in cubic centimeters will double.
### 3. If we double the radius of the glass, how would this affect the volume in cm? Why?
Using the same formula for volume:
If we double the radius \( r \), the new radius will be \( 2r \), and the volume will be:
\[ V' = \pi (2r)^2 h = \pi (4r^2) h = 4 \times (\pi r^2 h) \]
Thus, by doubling the radius, the volume of the glass will quadruple. Hence, doubling the radius while keeping the height constant will result in a volume that is four times larger.
### 4. How many cubic feet of grain can the silo hold?
Given the dimensions of the silo:
- Height \( h = 15 \) ft
- Radius \( r = 8 \) ft
- We can calculate the volume of a cylindrical silo using the formula:
\[ V = \pi r^2 h \]
Substituting the values in:
\[ V = \pi (8)^2 (15) \]
\[ V = \pi (64)(15) \]
\[ V = \pi (960) \]
Now, using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 960 \approx 3015.93 \text{ cubic feet} \]
So, the silo can hold approximately **3015.93 cubic feet** of grain.
If you need any further clarifications or if you can provide specific values for the volume of glass #1, that would be great!
### 1. How many ounces of tea will fill the glass in #1 if 1 cm³ = 0.0338 ounces?
Assuming you have the volume of the glass in cubic centimeters (cm³) from glass #1, you can convert this volume into ounces using the conversion factor you've provided. The formula to convert cm³ to ounces is:
\[ \text{Ounces} = \text{Volume (cm³)} \times 0.0338 \]
If you provide the volume of glass #1, I can calculate the exact amount.
### 2. If we double the height of the glass, how would this affect the volume in cm? Why?
The volume \( V \) of a cylindrical glass can be calculated using the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius.
- \( h \) is the height.
If you double the height \( h \), the new height will be \( 2h \), and the new volume will be:
\[ V' = \pi r^2 (2h) = 2 \times (\pi r^2 h) \]
This shows that when you double the height of the glass, the volume of the glass will also double. Therefore, the effect of doubling the height is that the volume in cubic centimeters will double.
### 3. If we double the radius of the glass, how would this affect the volume in cm? Why?
Using the same formula for volume:
If we double the radius \( r \), the new radius will be \( 2r \), and the volume will be:
\[ V' = \pi (2r)^2 h = \pi (4r^2) h = 4 \times (\pi r^2 h) \]
Thus, by doubling the radius, the volume of the glass will quadruple. Hence, doubling the radius while keeping the height constant will result in a volume that is four times larger.
### 4. How many cubic feet of grain can the silo hold?
Given the dimensions of the silo:
- Height \( h = 15 \) ft
- Radius \( r = 8 \) ft
- We can calculate the volume of a cylindrical silo using the formula:
\[ V = \pi r^2 h \]
Substituting the values in:
\[ V = \pi (8)^2 (15) \]
\[ V = \pi (64)(15) \]
\[ V = \pi (960) \]
Now, using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 960 \approx 3015.93 \text{ cubic feet} \]
So, the silo can hold approximately **3015.93 cubic feet** of grain.
If you need any further clarifications or if you can provide specific values for the volume of glass #1, that would be great!