The formula to find the surface area of a cube is 6 times the side length squared.
So, the total surface area of the storage bin would be:
6 * (5 cm)^2 = 6 * 25 cm^2 = 150 cm^2
Therefore, the total surface area of the storage bin is 150 square centimeters.
Manny created a storage bin for the family to hold the remote control and cell phone cords. What is the total surface area of the storage bin
Each side of the cube is 5 cm
11 answers
For Monica’s 14th birthday, she wants to make over her bedroom. The first phase in the bedroom makeover is painting her room. If Monica’s room is 20 ft. long, 15 ft. wide, and 9 ft. high, find the surface area of the room that you are going to paint, including the floor and ceiling(1 point)
To find the total surface area of the room that Monica wants to paint, including the floor and ceiling, we need to calculate the surface area of all six sides of the rectangular prism.
1. Surface area of the floor and ceiling:
- The floor area = length * width = 20 ft * 15 ft = 300 sq ft
- The ceiling has the same area as the floor, so the total area of the floor and ceiling is 2 * 300 sq ft = 600 sq ft
2. Surface area of the four walls:
- Two pairs of walls (front/back and left/right) have the same area.
- The area of the front/back walls = 2 * height * length = 2 * 9 ft * 20 ft = 360 sq ft
- The area of the left/right walls = 2 * height * width = 2 * 9 ft * 15 ft = 270 sq ft
- The total area of the four walls = 2 * (360 sq ft + 270 sq ft) = 2 * 630 sq ft = 1260 sq ft
3. Total surface area to paint:
- The total surface area to paint is the sum of the areas of the floor, ceiling, and walls.
- Total surface area = 600 sq ft (floor and ceiling) + 1260 sq ft (four walls) = 1860 sq ft
Therefore, the surface area of the room that Monica wants to paint, including the floor and ceiling, is 1860 square feet.
1. Surface area of the floor and ceiling:
- The floor area = length * width = 20 ft * 15 ft = 300 sq ft
- The ceiling has the same area as the floor, so the total area of the floor and ceiling is 2 * 300 sq ft = 600 sq ft
2. Surface area of the four walls:
- Two pairs of walls (front/back and left/right) have the same area.
- The area of the front/back walls = 2 * height * length = 2 * 9 ft * 20 ft = 360 sq ft
- The area of the left/right walls = 2 * height * width = 2 * 9 ft * 15 ft = 270 sq ft
- The total area of the four walls = 2 * (360 sq ft + 270 sq ft) = 2 * 630 sq ft = 1260 sq ft
3. Total surface area to paint:
- The total surface area to paint is the sum of the areas of the floor, ceiling, and walls.
- Total surface area = 600 sq ft (floor and ceiling) + 1260 sq ft (four walls) = 1860 sq ft
Therefore, the surface area of the room that Monica wants to paint, including the floor and ceiling, is 1860 square feet.
Christian collects model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h =9 inches, b =17 inches, s1 =10 inches, s2 =12 inches, s3 = 17 and l =10 inches.(1 point)
To find the surface area of the triangular prism display showcase, we need to calculate the areas of all the surfaces of the prism.
1. Base area of the triangular prism:
The base of the triangular prism is a triangle with a base (b) of 17 inches and height (h) of 9 inches. The formula to find the area of a triangle is 0.5 * base * height.
Base area = 0.5 * 17 in * 9 in = 76.5 square inches
2. Lateral surface area of the triangular prism:
The lateral surface area of a triangular prism can be calculated by adding the areas of all three rectangular faces that represent the sides of the prism. For a triangular prism, the lateral surface area is given by the sum of the three rectangles: s1 x l, s2 x l, and s3 x l.
Lateral surface area = s1 x l + s2 x l + s3 x l
Lateral surface area = 10 in x 10 in + 12 in x 10 in + 17 in x 10 in
Lateral surface area = 100 square inches + 120 square inches + 170 square inches
Lateral surface area = 390 square inches
3. Total surface area of the triangular prism:
The total surface area of the triangular prism is the sum of the base area and the lateral surface area.
Total surface area = Base area + Lateral surface area
Total surface area = 76.5 square inches + 390 square inches
Total surface area = 466.5 square inches
Therefore, the surface area of Christian's display showcase, shaped like a triangular prism, is 466.5 square inches.
1. Base area of the triangular prism:
The base of the triangular prism is a triangle with a base (b) of 17 inches and height (h) of 9 inches. The formula to find the area of a triangle is 0.5 * base * height.
Base area = 0.5 * 17 in * 9 in = 76.5 square inches
2. Lateral surface area of the triangular prism:
The lateral surface area of a triangular prism can be calculated by adding the areas of all three rectangular faces that represent the sides of the prism. For a triangular prism, the lateral surface area is given by the sum of the three rectangles: s1 x l, s2 x l, and s3 x l.
Lateral surface area = s1 x l + s2 x l + s3 x l
Lateral surface area = 10 in x 10 in + 12 in x 10 in + 17 in x 10 in
Lateral surface area = 100 square inches + 120 square inches + 170 square inches
Lateral surface area = 390 square inches
3. Total surface area of the triangular prism:
The total surface area of the triangular prism is the sum of the base area and the lateral surface area.
Total surface area = Base area + Lateral surface area
Total surface area = 76.5 square inches + 390 square inches
Total surface area = 466.5 square inches
Therefore, the surface area of Christian's display showcase, shaped like a triangular prism, is 466.5 square inches.
Find the surface area of a cube with sides measuring 11 meters.(1 point)
The formula to find the surface area of a cube is 6 * side^2, where side is the length of each side of the cube.
Given that each side of the cube measures 11 meters, we can plug this value into the formula:
Surface area = 6 * (11 m)^2
Surface area = 6 * 121 m^2
Surface area = 726 m^2
Therefore, the surface area of a cube with sides measuring 11 meters is 726 square meters.
Given that each side of the cube measures 11 meters, we can plug this value into the formula:
Surface area = 6 * (11 m)^2
Surface area = 6 * 121 m^2
Surface area = 726 m^2
Therefore, the surface area of a cube with sides measuring 11 meters is 726 square meters.
Cherese needs to buy some cardboard to build a box 10 inches long, 9 inches wide, and 7 inches high. If she purchases 500 square inches of cardboard, how much will be left over?(1 point)
To find the amount of cardboard Cherese will use to build the box, we need to calculate the surface area of the box first and then subtract that from the total amount of cardboard purchased.
The surface area of the box can be found by adding the areas of each side of the box:
- 2 * (length * width) + 2 * (width * height) + 2 * (length * height)
- 2 * (10 in * 9 in) + 2 * (9 in * 7 in) + 2 * (10 in * 7 in)
- 2 * 90 sq in + 2 * 63 sq in + 2 * 70 sq in
- 180 sq in + 126 sq in + 140 sq in
- 446 sq in
Cherese will use 446 square inches of cardboard to build the box. If she purchased 500 square inches, the amount left over would be:
500 sq in - 446 sq in = 54 sq in
Therefore, Cherese will have 54 square inches of cardboard left over after building the box.
The surface area of the box can be found by adding the areas of each side of the box:
- 2 * (length * width) + 2 * (width * height) + 2 * (length * height)
- 2 * (10 in * 9 in) + 2 * (9 in * 7 in) + 2 * (10 in * 7 in)
- 2 * 90 sq in + 2 * 63 sq in + 2 * 70 sq in
- 180 sq in + 126 sq in + 140 sq in
- 446 sq in
Cherese will use 446 square inches of cardboard to build the box. If she purchased 500 square inches, the amount left over would be:
500 sq in - 446 sq in = 54 sq in
Therefore, Cherese will have 54 square inches of cardboard left over after building the box.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
The prism is 5 cm in height, 9 cm in width, and 12 cm in length. There is also 13 cm from Dow to up of the wedge of the cheese
The prism is 5 cm in height, 9 cm in width, and 12 cm in length. There is also 13 cm from Dow to up of the wedge of the cheese
To calculate the amount of plastic wrap needed to cover the wedge of cheese, we need to find the lateral surface area of the triangular prism.
Given:
- Height (h) = 5 cm
- Width (w) = 9 cm
- Length (l) = 12 cm
- Diagonal (d) = 13 cm
First, we need to calculate the slant height (s) of the triangular prism, which is the distance from the top edge to the bottom corner (Dow to up):
s = √(h^2 + l^2)
s = √(5^2 + 12^2)
s = √(25 + 144)
s = √169
s = 13 cm
The lateral surface area (A) of the triangular prism can be calculated using the formula for lateral surface area of a triangular prism:
A = Perimeter of the base * slant height
A = (w + l) * s
A = (9 cm + 12 cm) * 13 cm
A = 21 cm * 13 cm
A = 273 cm^2
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is 273 square centimeters.
Given:
- Height (h) = 5 cm
- Width (w) = 9 cm
- Length (l) = 12 cm
- Diagonal (d) = 13 cm
First, we need to calculate the slant height (s) of the triangular prism, which is the distance from the top edge to the bottom corner (Dow to up):
s = √(h^2 + l^2)
s = √(5^2 + 12^2)
s = √(25 + 144)
s = √169
s = 13 cm
The lateral surface area (A) of the triangular prism can be calculated using the formula for lateral surface area of a triangular prism:
A = Perimeter of the base * slant height
A = (w + l) * s
A = (9 cm + 12 cm) * 13 cm
A = 21 cm * 13 cm
A = 273 cm^2
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is 273 square centimeters.
1 answer