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

Question

An animated image showing the geometric visualization of a right circular cylinder where the height is indicated to be 28 cm and the diameter is defined to be 15.5 cm. The cylinder, appearing like a roll of paper, rests horizontally on a neutral background. Emphasize the measurements and the 3D form of the cylinder visually so that viewers understand the task. The image should aim to illustrate the concept of calculating the surface area.

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

1,362.76 cm2
1,362.76 cm squared

4,234.29 cm2
4,234.29 cm squared

1,508.77 cm2
1,508.77 cm squared

1,739.95 cm2

Answer 1

To find the surface area of a right circular cylinder, you need to find the lateral surface area and the two circular bases.

The lateral surface area is given by the formula: Lateral Surface Area = 2πrh, where r is the radius and h is the height.

First, find the radius of the cylinder using the diameter: r = 15.5 cm / 2 = 7.75 cm.

Now, calculate the lateral surface area: Lateral Surface Area = 2 * 3.14 * 7.75 cm * 28 cm = 1,362.76 cm2.

The two circular bases have an area of πr^2. Calculate this for the two bases: 2 * π * (7.75 cm)^2 = 2 * 3.14 * 60.06 cm2 = 376.72 cm2.

Finally, add the lateral surface area and the two circular bases to get the total surface area: 1,362.76 cm2 + 376.72 cm2 = 1,739.95 cm2.

Aleksandr, the correct answer is 1,739.95 cm2.

Answer 2

To find the surface area of the steel rod, you need to find the lateral surface area and the two circular bases.

First, calculate the radius of the cylinder using the diameter: r = 0.50 inches / 2 = 0.25 inches.

Now, calculate the lateral surface area: Lateral Surface Area = 2 * 3.14 * r * h = 2 * 3.14 * 0.25 inches * 36 inches = 56.52 inches2.

Next, calculate the area of the two circular bases: 2 * 3.14 * (0.25 inches)^2 = 2 * 3.14 * 0.0625 square inches = 0.39 square inches.

Finally, add the lateral surface area and the two circular bases to get the total surface area: 56.52 inches2 + 0.39 square inches = 56.91 inches2.

Maria, the correct answer is 56.91 inches2.

Answer 3

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)
Responses

1,287.88 inches2
1,287.88 inches squared

163.28 inches2
163.28 inches squared

265.33 inches2
265.33 inches squared

428.61 inches2

Answer 4

To find the surface area of the cake in the shape of a right circular cylinder, you need to find the lateral surface area and the two circular bases.

First, calculate the radius of the cake using the diameter: r = 13 inches / 2 = 6.5 inches.

Now, calculate the lateral surface area: Lateral Surface Area = 2 * 3.14 * r * h = 2 * 3.14 * 6.5 inches * 4 inches = 163.28 inches2.

Next, calculate the area of the two circular bases: 2 * 3.14 * (6.5 inches)^2 = 2 * 3.14 * 42.25 square inches = 265.33 square inches.

Finally, add the lateral surface area and the two circular bases to get the total surface area needed to frost: 163.28 inches2 + 265.33 square inches = 428.61 inches2.

Marco, the correct answer is 428.61 inches2.

Answer 5

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 point)
Responses

56.91 inches2
56.91 inches squared

0.39 inches2
0.39 inches squared

56.52 inches2
56.52 inches squared

114.61 inches2