Surface Area: Apply
Show What You Know
Using your knowledge of surface area, answer the following questions.
Find the surface area of the cube that follows this list.
Find the surface area of the square pyramid that follows this list.
Write 1–2 sentences comparing the surface areas of the cube and the square pyramid that follows this list.
Find the surface area of the rectangular prism that follows this list.
Find the surface area of the rectangular pyramid that follows this list.
Write 1–2 sentences comparing the surface areas of the rectangular prism and the rectangular pyramid that follows this list.
Cube
An illustration shows a cube with a side length of 11 centimeters. The top, front, and right faces are visible. The faces and edges that are not visible are indicated by dashed lines.
Square Pyramid
An illustration shows a square pyramid. The front and right faces are visible. Faces and edges that are not visible are indicated by dashed lines.
The figure has a base length measuring 11 centimeters. A perpendicular, dashed line from the top vertex to the center of the base of the right face shows a slant height measuring 14 centimeters.
Rectangular Prism
An illustration shows a rectangular prism. The top, front, and right faces are visible. The edges and faces that are not visible are indicated by dashed lines.
The length measures 10 centimeters, the width measures 6 centimeters, and the height measures 12 centimeters.
Rectangular Pyramid
An illustration shows a rectangular pyramid. The front and right faces are visible. The edges and faces that are not visible are indicated by dashed lines.
Surface Area of Cube:
The surface area of a cube is calculated by finding the area of one face and multiplying it by 6 (since a cube has 6 faces that are all equal in size). The area of one face is found by multiplying the length of the side by itself (11 cm x 11 cm = 121 sq cm). Therefore, the surface area of the cube is 121 sq cm x 6 = 726 sq cm.
Surface Area of Square Pyramid:
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the 4 triangles that make up the sides. The area of the base is found by multiplying the length of one side by itself (11 cm x 11 cm = 121 sq cm). The area of one triangle can be found using the formula 1/2 x base x height, so 1/2 x 11 cm x 14 cm = 77 sq cm. There are 4 triangles, so the total area for the sides is 77 sq cm x 4 = 308 sq cm. Adding the base and side areas gives a total surface area of 121 sq cm + 308 sq cm = 429 sq cm.
Comparing Cube and Square Pyramid Surface Areas:
The surface area of the cube is 726 sq cm, while the surface area of the square pyramid is 429 sq cm. This means that the cube has a larger surface area compared to the square pyramid.
Surface Area of Rectangular Prism:
The surface area of a rectangular prism is calculated by finding the area of each face and then adding them together. The area of the top and bottom faces are length x width (10 cm x 6 cm = 60 sq cm for each face), and the area of the front and back faces are length x height (10 cm x 12 cm = 120 sq cm for each face). The area of the right and left faces are width x height (6 cm x 12 cm = 72 sq cm for each face). Adding all the areas together gives a total surface area of 60 sq cm + 60 sq cm + 120 sq cm + 120 sq cm + 72 sq cm + 72 sq cm = 504 sq cm.
Surface Area of Rectangular Pyramid:
To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the 4 triangles that make up the sides. The base has an area of length x width (10 cm x 6 cm = 60 sq cm). The area of one triangle can be found using the formula 1/2 x base x height, so 1/2 x 10 cm x 14 cm = 70 sq cm. There are 4 triangles, so the total area for the sides is 70 sq cm x 4 = 280 sq cm. Adding the base and side areas gives a total surface area of 60 sq cm + 280 sq cm = 340 sq cm.
Comparing Rectangular Prism and Rectangular Pyramid Surface Areas:
The surface area of the rectangular prism is 504 sq cm, while the surface area of the rectangular pyramid is 340 sq cm. This means that the rectangular prism has a larger surface area compared to the rectangular pyramid.
Find the surface area of the cylinder net.
Surface Area = 2πr2+2πrh
Use π = 3.14
To find the surface area of a cylinder, we use the formula:
Surface Area = 2πr^2 + 2πrh
Given that π ≈ 3.14, we need to know the radius (r) and height (h) of the cylinder to calculate the surface area. Can you please provide those measurements?
7, 14, 7. (in)
Given the measurements of radius (r = 7 in) and height (h = 14 in), we can calculate the surface area of the cylinder using the formula:
Surface Area = 2πr^2 + 2πrh
Surface Area = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 14
Surface Area = 2 * 3.14 * 49 + 2 * 3.14 * 98
Surface Area = 6.28 * 49 + 6.28 * 98
Surface Area = 306.92 + 615.44
Surface Area ≈ 922.36 square inches
Therefore, the surface area of the cylinder with a radius of 7 inches and height of 14 inches is approximately 922.36 square inches.
wrong
I apologize for the error. Let's recalculate the surface area of the cylinder using the correct formula and measurements:
Given:
Radius (r) = 7 inches
Height (h) = 14 inches
π ≈ 3.14
Surface Area = 2πr^2 + 2πrh
Surface Area = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 14
Surface Area = 2 * 3.14 * 49 + 2 * 3.14 * 98
Surface Area = 2 * 3.14 * 49 + 2 * 3.14 * 98
Surface Area = 307.72 + 615.44
Surface Area = 923.16 square inches
Therefore, the correct surface area of the cylinder with a radius of 7 inches and height of 14 inches is approximately 923.16 square inches.