We appreciate your visit to A gallon is equivalent to 231 cubic inches Which of the following is closest to the diameter in inches of a cylindrical container with a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the diameter of a cylindrical container with a volume of 1 gallon and a height of 11 inches, we need to use the formula for the volume of a cylinder. The formula is:
[tex]\[ \text{Volume} = \pi r^2 h \][/tex]
Where:
- [tex]\( \pi \)[/tex] is a constant (approximately 3.14159),
- [tex]\( r \)[/tex] is the radius of the cylinder's base,
- [tex]\( h \)[/tex] is the height of the cylinder.
We know from the problem that:
- The volume of the cylinder (equivalent to 1 gallon) is 231 cubic inches,
- The height [tex]\( h \)[/tex] is 11 inches.
We need to find the radius [tex]\( r \)[/tex] first and then determine the diameter, which is twice the radius.
Step 1: Rearrange the volume formula to solve for the radius [tex]\( r \)[/tex].
[tex]\[ r^2 = \frac{\text{Volume}}{\pi h} \][/tex]
[tex]\[ r = \sqrt{\frac{\text{Volume}}{\pi h}} \][/tex]
Step 2: Substitute the given values into the formula.
Substitute the volume (231 cubic inches) and the height (11 inches) into the rearranged formula:
[tex]\[ r = \sqrt{\frac{231}{\pi \times 11}} \][/tex]
Step 3: Calculate the radius.
After performing the calculation inside the square root:
[tex]\[ r \approx 2.585 \text{ inches} \][/tex]
Step 4: Find the diameter.
The diameter is twice the radius:
[tex]\[ \text{Diameter} = 2r \][/tex]
[tex]\[ \text{Diameter} = 2 \times 2.585 \][/tex]
[tex]\[ \text{Diameter} \approx 5.171 \text{ inches} \][/tex]
Step 5: Select the closest option.
From the options provided:
- (A) 3
- (B) 5
- (C) 6
- (D) 8
- (E) 16
The value 5.171 is closest to option (B) 5.
Therefore, the closest diameter of the cylindrical container is [tex]\( 5 \)[/tex] inches. Option (B) is the correct answer.
[tex]\[ \text{Volume} = \pi r^2 h \][/tex]
Where:
- [tex]\( \pi \)[/tex] is a constant (approximately 3.14159),
- [tex]\( r \)[/tex] is the radius of the cylinder's base,
- [tex]\( h \)[/tex] is the height of the cylinder.
We know from the problem that:
- The volume of the cylinder (equivalent to 1 gallon) is 231 cubic inches,
- The height [tex]\( h \)[/tex] is 11 inches.
We need to find the radius [tex]\( r \)[/tex] first and then determine the diameter, which is twice the radius.
Step 1: Rearrange the volume formula to solve for the radius [tex]\( r \)[/tex].
[tex]\[ r^2 = \frac{\text{Volume}}{\pi h} \][/tex]
[tex]\[ r = \sqrt{\frac{\text{Volume}}{\pi h}} \][/tex]
Step 2: Substitute the given values into the formula.
Substitute the volume (231 cubic inches) and the height (11 inches) into the rearranged formula:
[tex]\[ r = \sqrt{\frac{231}{\pi \times 11}} \][/tex]
Step 3: Calculate the radius.
After performing the calculation inside the square root:
[tex]\[ r \approx 2.585 \text{ inches} \][/tex]
Step 4: Find the diameter.
The diameter is twice the radius:
[tex]\[ \text{Diameter} = 2r \][/tex]
[tex]\[ \text{Diameter} = 2 \times 2.585 \][/tex]
[tex]\[ \text{Diameter} \approx 5.171 \text{ inches} \][/tex]
Step 5: Select the closest option.
From the options provided:
- (A) 3
- (B) 5
- (C) 6
- (D) 8
- (E) 16
The value 5.171 is closest to option (B) 5.
Therefore, the closest diameter of the cylindrical container is [tex]\( 5 \)[/tex] inches. Option (B) is the correct answer.
Thanks for taking the time to read A gallon is equivalent to 231 cubic inches Which of the following is closest to the diameter in inches of a cylindrical container with a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
