Question
Using the measurements shown on each net, find the surface area of the cylinder. (Hint: SA = 2πr^2 + 2πrh) Drag and drop each surface area under the appropriate cylinder.
Drop target 1
Drop target 2
Drop target 3
Drop target 4
Drop target 1
Drop target 2
Drop target 3
Drop target 4
Answers
GPT 3.5
There are no measurements or net images provided. Please provide the measurements or net images so that we can help you find the surface area of the cylinder.
i need help finding the surface area of each cylinder
cylinder 1 has a radius of 7 cm and a height of 11 cm
cylinder 2 has a radius of 4 cm and a height of 4 cm
cylinder 3 has a radius of 3 cm and a height of 5 cm
cylinder 4 has a radius of 2 cm and a height of 3 cm
I need each surface area for each cylinder
cylinder 1 has a radius of 7 cm and a height of 11 cm
cylinder 2 has a radius of 4 cm and a height of 4 cm
cylinder 3 has a radius of 3 cm and a height of 5 cm
cylinder 4 has a radius of 2 cm and a height of 3 cm
I need each surface area for each cylinder
GPT 3.5
Sure! Let's find the surface area for each of the given cylinders using the formula SA = 2πr^2 + 2πrh.
Cylinder 1:
Radius (r) = 7 cm
Height (h) = 11 cm
Surface area = 2π(7^2) + 2π(7)(11)
= 2π(49) + 2π(77)
= 98π + 154π
= 252π cm^2
Cylinder 2:
Radius (r) = 4 cm
Height (h) = 4 cm
Surface area = 2π(4^2) + 2π(4)(4)
= 2π(16) + 2π(16)
= 32π + 32π
= 64π cm^2
Cylinder 3:
Radius (r) = 3 cm
Height (h) = 5 cm
Surface area = 2π(3^2) + 2π(3)(5)
= 2π(9) + 2π(15)
= 18π + 30π
= 48π cm^2
Cylinder 4:
Radius (r) = 2 cm
Height (h) = 3 cm
Surface area = 2π(2^2) + 2π(2)(3)
= 2π(4) + 2π(6)
= 8π + 12π
= 20π cm^2
So, the surface areas for the given cylinders are:
- Cylinder 1: 252π cm^2
- Cylinder 2: 64π cm^2
- Cylinder 3: 48π cm^2
- Cylinder 4: 20π cm^2
Cylinder 1:
Radius (r) = 7 cm
Height (h) = 11 cm
Surface area = 2π(7^2) + 2π(7)(11)
= 2π(49) + 2π(77)
= 98π + 154π
= 252π cm^2
Cylinder 2:
Radius (r) = 4 cm
Height (h) = 4 cm
Surface area = 2π(4^2) + 2π(4)(4)
= 2π(16) + 2π(16)
= 32π + 32π
= 64π cm^2
Cylinder 3:
Radius (r) = 3 cm
Height (h) = 5 cm
Surface area = 2π(3^2) + 2π(3)(5)
= 2π(9) + 2π(15)
= 18π + 30π
= 48π cm^2
Cylinder 4:
Radius (r) = 2 cm
Height (h) = 3 cm
Surface area = 2π(2^2) + 2π(2)(3)
= 2π(4) + 2π(6)
= 8π + 12π
= 20π cm^2
So, the surface areas for the given cylinders are:
- Cylinder 1: 252π cm^2
- Cylinder 2: 64π cm^2
- Cylinder 3: 48π cm^2
- Cylinder 4: 20π cm^2
the choices they gave me were 150.8 cm^2 62.8 cm^2 201 cm^2 and 791.7 cm^2
GPT 3.5
Apologies for the confusion. Let's calculate the surface area for each cylinder again and compare it with the given choices.
Cylinder 1:
Radius (r) = 7 cm
Height (h) = 11 cm
Surface area = 2π(7^2) + 2π(7)(11)
= 2π(49) + 2π(77)
= 98π + 154π
= 252π cm^2
The surface area for Cylinder 1 is 252π cm^2. Approximating π to 3.14, we have:
252π cm^2 = 252(3.14) cm^2
= 791.68 cm^2
The closest choice to 791.68 cm^2 is 791.7 cm^2.
Therefore, we can match Cylinder 1 with the choice 791.7 cm^2.
Calculating the surface area of the remaining cylinders:
Cylinder 2:
Radius (r) = 4 cm
Height (h) = 4 cm
Surface area = 2π(4^2) + 2π(4)(4)
= 2π(16) + 2π(16)
= 32π + 32π
= 64π cm^2
The surface area for Cylinder 2 is 64π cm^2. Approximating π to 3.14, we have:
64π cm^2 = 64(3.14) cm^2
= 200.96 cm^2
The closest choice to 200.96 cm^2 is 201 cm^2.
Therefore, we can match Cylinder 2 with the choice 201 cm^2.
Calculating the surface area for the remaining cylinders:
Cylinder 3:
Radius (r) = 3 cm
Height (h) = 5 cm
Surface area = 2π(3^2) + 2π(3)(5)
= 2π(9) + 2π(15)
= 18π + 30π
= 48π cm^2
The surface area for Cylinder 3 is 48π cm^2. Approximating π to 3.14, we have:
48π cm^2 = 48(3.14) cm^2
= 150.72 cm^2
The closest choice to 150.72 cm^2 is 150.8 cm^2.
Therefore, we can match Cylinder 3 with the choice 150.8 cm^2.
Calculating the surface area for Cylinder 4:
Cylinder 4:
Radius (r) = 2 cm
Height (h) = 3 cm
Surface area = 2π(2^2) + 2π(2)(3)
= 2π(4) + 2π(6)
= 8π + 12π
= 20π cm^2
The surface area for Cylinder 4 is 20π cm^2. Approximating π to 3.14, we have:
20π cm^2 = 20(3.14) cm^2
= 62.8 cm^2
Therefore, we can match Cylinder 4 with the choice 62.8 cm^2.
Matching the cylinders with the given choices:
- Cylinder 1: 791.7 cm^2
- Cylinder 2: 201 cm^2
- Cylinder 3: 150.8 cm^2
- Cylinder 4: 62.8 cm^2
Cylinder 1:
Radius (r) = 7 cm
Height (h) = 11 cm
Surface area = 2π(7^2) + 2π(7)(11)
= 2π(49) + 2π(77)
= 98π + 154π
= 252π cm^2
The surface area for Cylinder 1 is 252π cm^2. Approximating π to 3.14, we have:
252π cm^2 = 252(3.14) cm^2
= 791.68 cm^2
The closest choice to 791.68 cm^2 is 791.7 cm^2.
Therefore, we can match Cylinder 1 with the choice 791.7 cm^2.
Calculating the surface area of the remaining cylinders:
Cylinder 2:
Radius (r) = 4 cm
Height (h) = 4 cm
Surface area = 2π(4^2) + 2π(4)(4)
= 2π(16) + 2π(16)
= 32π + 32π
= 64π cm^2
The surface area for Cylinder 2 is 64π cm^2. Approximating π to 3.14, we have:
64π cm^2 = 64(3.14) cm^2
= 200.96 cm^2
The closest choice to 200.96 cm^2 is 201 cm^2.
Therefore, we can match Cylinder 2 with the choice 201 cm^2.
Calculating the surface area for the remaining cylinders:
Cylinder 3:
Radius (r) = 3 cm
Height (h) = 5 cm
Surface area = 2π(3^2) + 2π(3)(5)
= 2π(9) + 2π(15)
= 18π + 30π
= 48π cm^2
The surface area for Cylinder 3 is 48π cm^2. Approximating π to 3.14, we have:
48π cm^2 = 48(3.14) cm^2
= 150.72 cm^2
The closest choice to 150.72 cm^2 is 150.8 cm^2.
Therefore, we can match Cylinder 3 with the choice 150.8 cm^2.
Calculating the surface area for Cylinder 4:
Cylinder 4:
Radius (r) = 2 cm
Height (h) = 3 cm
Surface area = 2π(2^2) + 2π(2)(3)
= 2π(4) + 2π(6)
= 8π + 12π
= 20π cm^2
The surface area for Cylinder 4 is 20π cm^2. Approximating π to 3.14, we have:
20π cm^2 = 20(3.14) cm^2
= 62.8 cm^2
Therefore, we can match Cylinder 4 with the choice 62.8 cm^2.
Matching the cylinders with the given choices:
- Cylinder 1: 791.7 cm^2
- Cylinder 2: 201 cm^2
- Cylinder 3: 150.8 cm^2
- Cylinder 4: 62.8 cm^2
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