We appreciate your visit to A right cylinder has a circumference of tex 16 pi text cm tex Its height is half the radius Identify the lateral area and the. 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 solve the problem, we need to find the lateral area and the surface area of the right cylinder.
Step 1: Determine the radius of the cylinder.
The circumference of the base of the cylinder is given as [tex]\(16 \pi \, \text{cm}\)[/tex].
The formula for the circumference of a circle is:
[tex]\[ C = 2 \pi r \][/tex]
So, we set up the equation:
[tex]\[ 16 \pi = 2 \pi r \][/tex]
To find the radius [tex]\(r\)[/tex], divide both sides by [tex]\(2 \pi\)[/tex]:
[tex]\[ r = \frac{16 \pi}{2 \pi} = 8 \, \text{cm} \][/tex]
Step 2: Determine the height of the cylinder.
We are told that the height [tex]\(h\)[/tex] is half of the radius:
[tex]\[ h = \frac{1}{2} \times 8 = 4 \, \text{cm} \][/tex]
Step 3: Calculate the lateral area of the cylinder.
The formula for the lateral area [tex]\(L\)[/tex] of a cylinder is:
[tex]\[ L = 2 \pi r h \][/tex]
Substitute the values for [tex]\(r\)[/tex] and [tex]\(h\)[/tex]:
[tex]\[ L = 2 \pi \times 8 \times 4 = 201.1 \, \text{cm}^2 \][/tex] (rounded to one decimal place)
Step 4: Calculate the surface area of the cylinder.
The surface area [tex]\(S\)[/tex] is the sum of the lateral area and the area of the two circular bases. The formula for the surface area is:
[tex]\[ S = L + 2 \pi r^2 \][/tex]
First, calculate the area of the two bases:
[tex]\[ 2 \pi r^2 = 2 \pi \times 8^2 = 128 \pi \][/tex]
So:
[tex]\[ S = 201.1 + 128 \pi = 603.2 \, \text{cm}^2 \][/tex] (rounded to one decimal place)
So, the lateral area is approximately [tex]\(201.1 \, \text{cm}^2\)[/tex] and the surface area is approximately [tex]\(603.2 \, \text{cm}^2\)[/tex].
The correct choice is:
[tex]\[ L \approx 201.1 \, \text{cm}^2 ; S \approx 603.2 \, \text{cm}^2 \][/tex]
Step 1: Determine the radius of the cylinder.
The circumference of the base of the cylinder is given as [tex]\(16 \pi \, \text{cm}\)[/tex].
The formula for the circumference of a circle is:
[tex]\[ C = 2 \pi r \][/tex]
So, we set up the equation:
[tex]\[ 16 \pi = 2 \pi r \][/tex]
To find the radius [tex]\(r\)[/tex], divide both sides by [tex]\(2 \pi\)[/tex]:
[tex]\[ r = \frac{16 \pi}{2 \pi} = 8 \, \text{cm} \][/tex]
Step 2: Determine the height of the cylinder.
We are told that the height [tex]\(h\)[/tex] is half of the radius:
[tex]\[ h = \frac{1}{2} \times 8 = 4 \, \text{cm} \][/tex]
Step 3: Calculate the lateral area of the cylinder.
The formula for the lateral area [tex]\(L\)[/tex] of a cylinder is:
[tex]\[ L = 2 \pi r h \][/tex]
Substitute the values for [tex]\(r\)[/tex] and [tex]\(h\)[/tex]:
[tex]\[ L = 2 \pi \times 8 \times 4 = 201.1 \, \text{cm}^2 \][/tex] (rounded to one decimal place)
Step 4: Calculate the surface area of the cylinder.
The surface area [tex]\(S\)[/tex] is the sum of the lateral area and the area of the two circular bases. The formula for the surface area is:
[tex]\[ S = L + 2 \pi r^2 \][/tex]
First, calculate the area of the two bases:
[tex]\[ 2 \pi r^2 = 2 \pi \times 8^2 = 128 \pi \][/tex]
So:
[tex]\[ S = 201.1 + 128 \pi = 603.2 \, \text{cm}^2 \][/tex] (rounded to one decimal place)
So, the lateral area is approximately [tex]\(201.1 \, \text{cm}^2\)[/tex] and the surface area is approximately [tex]\(603.2 \, \text{cm}^2\)[/tex].
The correct choice is:
[tex]\[ L \approx 201.1 \, \text{cm}^2 ; S \approx 603.2 \, \text{cm}^2 \][/tex]
Thanks for taking the time to read A right cylinder has a circumference of tex 16 pi text cm tex Its height is half the radius Identify the lateral area and the. 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
