Surface Area of Cylinders Quick Check
3 of 53 of 5 Items
Question
Aleksandr has a roll of paper that is in the shape of a right circular cylinder. It has a height of 28 cm and a diameter of 15.5 cm. Help Aleksandr solve for the surface area. Use 3.14 for π .(1 point)
Responses
1,739.95 cm2
1,739.95 cm squared
4,234.29 cm2
4,234.29 cm squared
1,362.76 cm2
1,362.76 cm squared
1,508.77 cm2
1,508.77 cm squared
To calculate the surface area of the right circular cylinder, we first need to find the radius of the cylinder. The radius is half the diameter, so the radius is 15.5 cm / 2 = 7.75 cm.
Now, we can calculate the surface area using the formula: 2πr² + 2πrh, where r is the radius, h is the height, and π is approximately 3.14.
Surface Area = 2 * 3.14 * (7.75)^2 + 2 * 3.14 * 7.75 * 28
Surface Area = 2 * 3.14 * 60.0625 + 2 * 3.14 * 217
Surface Area = 376.990625 + 1363.36
Surface Area = 1740.350625
Rounded to the nearest hundredth, the surface area of the right circular cylinder is approximately 1,740.35 cm².
Therefore, the closest answer choice is: 1,739.95 cm².
Surface Area of Cylinders Quick Check
3 of 53 of 5 Items
Question
Aleksandr has a roll of paper that is in the shape of a right circular cylinder. It has a height of 28 cm and a diameter of 15.5 cm. Help Aleksandr solve for the surface area. Use 3.14 for π.(1 point)
Responses
To find the surface area of the cylinder, we can follow these steps:
1. Calculate the radius (r) using the given diameter:
r = diameter / 2
r = 15.5 cm / 2
r = 7.75 cm
2. Calculate the lateral surface area (A_lateral) of the cylinder:
A_lateral = 2 * π * r * h
A_lateral = 2 * 3.14 * 7.75 cm * 28 cm
A_lateral = 2 * 3.14 * 217 cm
A_lateral = 1361.36 cm²
3. Calculate the surface area of the two bases (A_bases) of the cylinder:
A_bases = 2 * π * r²
A_bases = 2 * 3.14 * (7.75 cm)²
A_bases = 2 * 3.14 * 60.0625 cm²
A_bases = 376.99 cm²
4. Add the lateral surface area and the surface area of the bases to find the total surface area (A_total):
A_total = A_lateral + A_bases
A_total = 1361.36 cm² + 376.99 cm²
A_total = 1738.35 cm²
Therefore, the surface area of the right circular cylinder is approximately 1738.35 cm².
The closest answer choice is: 1,739.95 cm²
Question
Maria wants to find the surface area of a steel rod that is in the shape of a right circular cylinder. The diameter is 0.50 inches, and the length is 36 inches. What is the surface area? Use 3.14 for π .(1 poi
To find the surface area of the steel rod, we can follow these steps:
1. Calculate the radius (r) using the given diameter:
r = diameter / 2
r = 0.50 inches / 2
r = 0.25 inches
2. Calculate the lateral surface area (A_lateral) of the cylinder:
A_lateral = 2 * π * r * h
A_lateral = 2 * 3.14 * 0.25 inches * 36 inches
A_lateral = 2 * 3.14 * 9 inches
A_lateral = 56.52 square inches
3. Calculate the surface area of the two bases (A_bases) of the cylinder:
A_bases = 2 * π * r²
A_bases = 2 * 3.14 * (0.25 inches)²
A_bases = 2 * 3.14 * 0.0625 square inches
A_bases = 0.3925 square inches
4. Add the lateral surface area and the surface area of the bases to find the total surface area (A_total):
A_total = A_lateral + A_bases
A_total = 56.52 square inches + 0.3925 square inches
A_total = 56.9125 square inches
Therefore, the surface area of the right circular cylinder (steel rod) is approximately 56.9125 square inches.
Surface Area of Cylinders Quick Check
5 of 55 of 5 Items
Question
Marco is baking a cake for a party. The cake is in the shape of a right circular cylinder. He needs to buy frosting for the cake but doesn’t know the surface area of the cake. If the diameter of the cake pan is 13 inches, and the height is 4 inches, what is the surface area he needs to frost? Use 3.14 for π .(1 point)
To find the surface area of the cake (right circular cylinder), we can follow these steps:
1. Calculate the radius (r) using the given diameter:
r = diameter / 2
r = 13 inches / 2
r = 6.5 inches
2. Calculate the lateral surface area (A_lateral) of the cylinder:
A_lateral = 2 * π * r * h
A_lateral = 2 * 3.14 * 6.5 inches * 4 inches
A_lateral = 2 * 3.14 * 26 inches
A_lateral = 163.76 square inches
3. Calculate the surface area of the two bases (A_bases) of the cylinder:
A_bases = 2 * π * r²
A_bases = 2 * 3.14 * (6.5 inches)²
A_bases = 2 * 3.14 * 42.25 square inches
A_bases = 265.45 square inches
4. Add the lateral surface area and the surface area of the bases to find the total surface area (A_total):
A_total = A_lateral + A_bases
A_total = 163.76 square inches + 265.45 square inches
A_total = 429.21 square inches
Therefore, the surface area of the right circular cylinder (cake) that Marco needs to frost is approximately 429.21 square inches.
so its 428.61 inches^2?
I apologize for the confusion in my previous response. Let's recalculate the total surface area for Marco's cake:
Given:
- Diameter = 13 inches
- Radius(r) = Diameter/2 = 13 inches / 2 = 6.5 inches
- Height(h) = 4 inches
1. Calculate the lateral surface area (A_lateral) of the cylinder:
A_lateral = 2 * π * r * h
A_lateral = 2 * 3.14 * 6.5 inches * 4 inches
A_lateral = 2 * 3.14 * 26 square inches
A_lateral = 163.76 square inches
2. Calculate the surface area of the two bases (A_bases) of the cylinder:
A_bases = 2 * π * r²
A_bases = 2 * 3.14 * (6.5 inches)²
A_bases = 2 * 3.14 * 42.25 square inches
A_bases = 265.45 square inches
3. Calculate the total surface area (A_total):
A_total = A_lateral + A_bases
A_total = 163.76 square inches + 265.45 square inches
A_total = 429.21 square inches
Therefore, the correct surface area of the right circular cylinder (cake) that Marco needs to frost is approximately 429.21 square inches, not 428.61 square inches. Thank you for pointing that out.